05 - Review in Analytic Geometry (2025)
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Mapúa Institute of Technology**We aren't endorsed by this school
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CE MATH14
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Jan 4, 2025
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ANALYTIC GEOMETRY CE Review 1 Dindo F. Esplana 811x83-y−=811x83-y+=811x83y+=811x83y−=ANALYTIC GEOMETRY INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 1 only. MULTIPLE CHOICE Line Segment •Distance between Two Points on a Plane 1.Find the distance between the points (4, 2) and (-5, 1). a.9.22 units c.9.17 unitsb.9.06 unitsd.9.11 units 2.Find the length of the line segment joining the points (-5, 3) and (4, 2). a.5.10 units c.9.06 unitsb.8.83 units d.10.30 units•Slope / Inclination of a Line 3.Find the slope of the line segment joining (-2, -4) and (5, -3). a.-1/7 c.1/7 b.-1/3 d.1/3 4.Find the slope of the line segment joining (-5, 3) and (4, 2). a.5/9 c.1/9b.-5/9 d.-1/95.Find the inclination of the line segment joining (-2, -4) and (5, -3). a.98.13c.171.87b.81.87d.8.136.Find the inclination of the line segment joining (-5, 3) and (4, 2). a.6.34c.173.66b.96.34d.83.66Line •Standard / General Form of Equation of a Line 7.What is the slope-intercept form of the equation 3x + 8y –11 = 0? (Ans. c)a.c.b.d.8.Find the distance between the intercepts of the line x + 2y –6 = 0. a.7.61 units c.6.17 units b.7.16 unita d.6.71 units•Lines Determined by Geometric Conditions 9.Find the equation of the line passing through the points (-5, 3) and (4, 2). a.x –9y + 22 = 0 c.x + 9y –22 = 0 b.x + 9y + 22 = 0 d.x –9y –22 = 0 10.Find the equation of the line with x and y intercepts of -1 and 7, respectively. a.7x + y –7 = 0 c.7x –y + 7 = 0 b.7x + y + 7 = 0 d.7x –y –7 = 0 11.What is the equation of the line that passes through (4, 0) and is parallel to the line x –y –2 = 0? a.x + y –4 = 0 c.x –y –4 = 0 b.x + y + 4 = 0 d.x –y + 4 = 0 12.Find the equation of the line passing through the point (-1, -3) and perpendicular to the line 3x + 4y –12 = 0. a.3x + 4y + 15 = 0 c.3x + 4y –15 = 0b.4x –3y –5 = 0d.4x –3y + 5 = 0 13.Determine the distance of a line segment from (5, 3) to the y-axis if the line segment has a slope of 3/2. a.8.56 units c.8.89 unitsb.8.70 units d.9.01 units 14.Find the equation of the line with slope of 2/3 and passes through the intersection of the lines x –2y + 4 = 0 and 4x –2y + 1 = 0. a.4x –6y –9 = 0 c.4x –6y + 11 = 0b.4x –6y + 9 = 0 d.4x –6y + 11 = 015.In the equation of a line y = mx + b, m is the slope and b is the y-intercept of the line. Find the value of m when x1= 7.50, x2= 12.50, y1= 8.50, and y2= 20.60. a.9.65 c.-9.65 b.2.42d.-2.42 •Distance from a Point to a Line 16.The distance from the point (2, 1) to the line 4x –3y + 5 = 0 is a.1 c.3b.2d.4 17.Find the distance of the point (-1, -3) from the line 3x + 4y –12 = 0. a.5.04 units c.5.40 units b.4.05 units d.4.50 units 18.The two points on the line 2x + 3y + 4 = 0 which are at a distance 2 units from the line 3x + 4y –6 = 0 are a.(-5.50, 1) and (-5, 2)b.(-44, 64) and (-5, 2) c.(64, -44) and (4, -4) d.(-8, -8) and (-16, -16) Situation 1:Line A has a slope of -4 and passes through the point (-20, -15). Line B has an x-intercept of 10 and y-intercept of 25. 19.Determine the distance of line A to the point (-20, -10). a.2.11units c.1.12 unitsb.2.21 units d.1.21 units20.Determine the point of intersection of the lines A and B. a.(80, 225) c.(-80, 225) b.(-80, -225) d.(80, -225) 21.Determine the equation of the line perpendicular to line A and passing through the intersection of the two lines. a.x –4y + 890 = 0 c.x –4y + 980 = 0 b.x –4y –890 = 0 d.x –4y –980 = 0 •Distance between Parallel Lines 22.Find the distance between the parallel lines 4x –9y –18 = 0 and 8x –18y + 11 = 0. a.3.29 units c.2.39 units b.3.92 units d.2.93 units•Angle between Two Lines 23.Find the angle between the line 2y –9x –18 = 0 and the x-axis. a.74.77c.44.47b.77.47d.47.7724.Find the acute angle between the lines 4x + 3y –24 = 0 and 7x –24y + 168 = 0. a.63.39c.69.39b.63.99d.69.93•Lines of Degree Higher than One 25.Find the area bounded by the curve 5x2y + 4xy2–20xy = 0. a.8 sq. units c.12 sq. unitsb.9 sq. units d.10 sq. unitsPolygons •Area of Polygons by Coordinates 26.Find the area of a triangle whose vertices are A(-3, -1), B(5, 3), and C(2, -8). a.38 sq. unitsc.32 sq. unitsb.36 sq. units d.34 sq. units 27.Find the area of a pentagon whose vertices are A(2, 8), B(-3, 2), C(1, -6), D(4, -1), E(7, -3). a.72 sq. units c.68 sq. unitsb.84 sq. units d.62 sq. units•Centroid of Polygons 28.The two vertices of a triangle are (3, -6) and (9, -4). Find the ordinate of the third vertex so that the centroid of the triangle lies on the origin. a.-12 c.10 b.3 d.629.A composite area consists of a rectangle with vertices at (4, 0), (10, 0), (10, 3), and (4, 3) and a triangle with vertices at (4, 3), (10, 3), and (6, 8). Find the distance of the centroid of the composite area from the y-axis. a.3.24 units c.2.80 unitsb.5.22 units d.6.85 units30.A small square, 5 cm by 5 cm, is cut out on one corner of a rectangular cardboard 20 cm wide by 30 cm long. How far from the uncut longer side is the centroid of the remaining area? a.9.56 cm c.9.48 cm b.9.35 cm d.9.67 cm 31.Find the centroid of a pentagon whose vertices are A(2, 8), B(-3, 2), C(1, -6), D(4, -1), E(7, -3). a.(3/2, 372/385) c.(-3/2, 372/385)b.(-3/2, 385/372) d.(3/2, 385/372)Circle •Standard / General Form of Equation of a Circle 32.Find the coordinates of the center of the circle x2+ y2–6x + 4y –23 = 0. a.(-3, -2) c.(3, -2) b.(-3, 2) d.(3, 2)33.What is the radius of the circle x2+ y2–10x + 4y –196 = 0? a.15 unitsc.17 unitsb.16 units d.14 units 34.Determine the length of the chord common to the circles x2+ y2= 64 and x2+ y2–16x = 0. a.14.92 units c.12.05 unitsb.13.86 unitsd.12.77 units 35.Determine the area enclosed by the curve x2+ y2–10x + 4y –196 = 0. a.47.12 sq. units c.37.70 sq. unitsb.706.86 sq. unitsd.452.39 sq. units 36.Find the shortest distance from the point (10, 7) to the curve x2+ y2–6x + 4y –23 = 0. a.15.30 units c.14.70 unitsb.17.40 unitsd.13.50 units 37.Find the distance from the point (5, 8) to the farthest point on the circle x2+ y2+ 6x –16 = 0. a.16.31 unitsc.6.31 unitsb.19.22 units d.9.22 units
ANALYTIC GEOMETRY CE Review 2 Dindo F. Esplana •Radical Axis / Radical Center 38.Determine the equation of the radical axis of the circles x2+ y2–10x –6y + 18 = 0 and x2+ y2–4x + 12y + 31 = 0. a.6x –18y + 13 = 0 c.6x –18y –13 = 0b.6x + 18y + 13 = 0d.none of the above 39.Determine the equation of the radical axis of the circles x2+ y2+ 16x –10y + 90 = 0 and x2+ y2–4x + 8y + 11 = 0. a.20x –18y + 101 = 0b.20x –18y –101 = 0 c.20x –18y + 79 = 0 d.none of the above40.Find the coordinates of the radical center of the circles x2+ y2+ 4x + 4y –28 = 0, x2+ y2–20x –4y + 88 = 0, and x2+ y2–8x –24y + 151 = 0. a.(227/72, 121/24)c.(-227/72, -121/24)b.(121/24, 227/72) d.(-121/24, -227/72) •Circles Determined by Geometric Conditions 41.Find the equation of a circle with center at (3, -2) and radius of 6 units. a.x2+ y2–6x + 4y –23 = 0 b.x2+ y2+ 6x + 4y –23 = 0 c.x2+ y2+ 6x –4y –23 = 0 d.x2+ y2–6x –4y –23 = 0 42.A circle passes through the points (2, 8), (-15, 1), and (9, -9). Find the ordinate of its center. a.-1 c.-3b.2 d.-443.Find the equation of the circle tangent to the lines 5x + 12y –161 = 0 and 12x + 5y –126 = 0 and passing through the point (-9, -11). a.x2+ y2+ 8x –2y –152 = 0b.x2+ y2–6x + 4y –212 = 0 c.x2+ y2+ 10x –2y –134 = 0 d.none of the above Parabola •Standard / General Form of Equation of a Parabola 44.Where is the vertex of the parabola x2= 4(y –2)? a.(2, 0) c.(0, 4)b.(4, 0) d.(0, 2)45.What is the length of the latus rectum of the curve x2= 20y? a.10 units c.5 unitsb.15 units d.20 units46.Determine the equation of the directrix of the curve x2= 16y. a.y + 4 = 0c.x + 4 = 0b.y –4 = 0 d.x –4 = 047.Determine the length of the latus rectum of the parabola x2–6x –12y –51 = 0. a.3 units c.4 unitsb.12 unitsd.16 units Situation 2:Two conics are given below: y2–6y –8x –7 = 0 4x2+ 4y2+ 48x –24y –181 = 0 48.Which of the following define the conics? a.ellipse and parabola b.hyperbola and circlec.ellipse and hyperbola d.parabola and circle49.Find the points of intersection of the conics.a.(1.65, 8.40) and (1.65, -2.40)b.(1.76, 8.48) and (1.76, -2.48) c.(1.84, 8.54) and (1.84, -2.54) d.(1.91, 8.59) and (1.91, -2.59) 50.Find the distance between the points of intersection of the conics.a.11.08 units c.10.80 unitsb.10.97 unitsd.11.18 units•Parabolas Determined by Geometric Conditions 51.Find the equation of the parabola with vertex at (4, -3) and focus at (-1, -3). a.y2–6y + 20x –107 = 0b.y2+ 6y + 20x –71 = 0 c.y2–6y –20x + 53 = 0 d.y2+ 6y –20x + 89 = 0 52.Find the equation of the parabola passing through the points A(-4, 1), B(1, 8), and C(3, -2) with axis parallel to the y axis. a.32y2–213y –105x + 239 = 0b.32y2–213y –105x –239 = 0 c.32x2+ 47x + 35y –359 = 0d.32x2+ 47x + 35y + 359 = 0 Ellipse •Standard / General Form of Equation of an Ellipse 53.What is the area enclosed by the curve 9x2+ 25y2–225 = 0? a.188.50 sq. units c.150.80 sq. units b.47.12 sq. unitsd.75.40 sq. units 54.Determine the length of the latus rectum of the curve 16x2+ 9y2+ 64x –144y + 496 = 0. a.9.33 units c.4.50 units b.6.00 units d.10.67 units 55.Find the ratio of the major axis to the minor axis of the ellipse 9x2+ 4y2–72x –24y –144 = 0. a.1.50c.2.50b.2.00 d.3.00 56.Find the distance between the foci of the curve 9x2+ 25y2+ 18x + 200y + 184 = 0. a.5 units c.7 unitsb.8 unitsd.6 units57.Find the ratio of the length of the minor axis to the length of the major axis of the ellipse 9x2+ 16y2–144 = 0. a.0.60 c.0.50b.0.25 d.0.75 58.Find the length of the latus rectum of the curve 36x2+ 9y2–36 = 0. a.4 units c.1 unit b.2 units d.8 units Situation 3:An ellipse has the equation 16x2+ 25y2+ 128x –150y + 381 = 0. 59.Determine the coordinates of the center of the ellipse. a.(4, -3) c.(-4, -3) b.(4, 3) d.(-4, 3) 60.Determine the distance between the foci. a.3.00 unitsc.4.50 unitsb.1.50 units d.6.00 units61.Determine the distance between the directrices. a.16.67 units c.5.56 unitsb.4.17 units d.8.33 units 62.What is the eccentricity of the curve 9x2+ 25y2–144x + 200y + 751 = 0? a.0.50 c.0.75b.0.60 d.0.80•Ellipses Determined by Geometric Conditions 63.If the curve Ax2+ By2+ F = 0 passes through (0, 3) and (4, 0), the curve is a/an a.parabola c.hyperbolab.ellipsed.circle 64.Find the equation of the ellipse with center at (5, 4), major axis 16 units, minor axis 10 units, and major axis parallel to the x axis. a.25x2+ 64y2–250x –512y + 49 = 0b.64x2+ 25y2–640x –200y + 400 = 0c.64x2+ 25y2–512x –250y + 49 = 0 d.25x2+ 64y2–200x –640y + 400 = 0Hyperbola •Standard / General Form of Equation of a Hyperbola 65.How far from the x-axis is one focus of the hyperbola x2–2y2+ 4x + 4y + 4 = 0? a.3.72 units c.2.73 units b.3.27 units d.2.37 units Situation 4:A hyperbola has the equation x2–4y2–8x + 64y –256 = 0. 66.Determine the coordinates of the center. a.(4, 8)c.(4, -8) b.(-4, -8) d.(-4, 8)67.Determine the distance between the vertices. a.4 units c.8 units b.6 units d.10 units68.Determine the distance between the foci. a.7.67 units c.8.94 units b.6.93 units d.7.26 unitsLocus of Points 69.A fixed circle with center at (8, 6) has a radius of 5 units. Find the equation of the locus of points connecting the center of circles tangent to the given fixed circle and the x-axis. a.x2–16x –22y + 75 = 0 b.x2–16x –22y –75 = 0 c.x2–16x + 22y + 75 = 0 d.x2–16x + 22y –75 = 0 70.The perimeter of a triangle is 20 units, and the points A(2, -3) and B(2, 3) are two of the vertices. Find the equation of the graph of the third vertex. a.40x2+ 49y2–196y –1,764 = 0b.49x2+ 40y2–196x –1,764 = 0 c.40x2+ 49y2–196y + 1,764 = 0d.49x2+ 40y2–196x + 1,764 = 0