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Compilation of Problems in Analytic Geometry

1. Find the equation of the directrix of the parabola y^2=16x.

2. The midpoint of the line segment between P1 and P2 (-2, 4) is P (2, -1). Find P1

3. Given an ellipse: (x^2)/36 + (y^2)/32=1. Determine the distance between foci.

4. Convert the θ = π/3 to the Cartesian equation.

5. Find the coordinates of the point P(2, 4) with respect to the translated axis with origin at (1, 3).

6. The segment from (-1, 4) to (2, -2) is extended three times its own length. Find the terminal point.

7. Determine B such that 3x + 2y – 7 = 0 is perpendicular to 2x – By + 2 = 0.

8. Find the value of k for which the equation x^2+y^2+4x-2y-k=0 represents a point circle.

9. What is the diameter of a circle described by 9x2+9y2=16?

10. The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth.

11. Point P(x, y) moves with a distance from point (0, 1) one-half of its distance from the line y = 4. What is the equation of the locus?

12. A line passes through point (2, 2). Find the equation of the line if the length of the line segment intercepted by the coordinate axis is √5.

13. Find the area of the triangle which the line 2x – 3y + 6 = 0 forms with the coordinate axes.

14. Determine the coordinates of the point which is three-fifths of the way from the point (2, -5) to the point (-3, 5).

15. Two vertices of a triangle are (2, 4) and (-2, 3) and the area is 2 square units. Find the locus of the third vertex.

16. If the points (-2, 3), (x, y), and (-3, 5) lie on a straight line, find the equation of the line.

17. Find the inclination of the line passing through (-5, 3) and (10, 7).

18. Find the distance of the directrix from the center of an ellipse if its major axis is 10 and its minor axis is 8.

19. A point moves so that its distance from the point (2, -1) is equal to its distance from the x-axis. What is the equation of the locus?

20. The parabolic antenna has an equation of y2+8x=0. Determine the length of the latus rectum.

21. Find the equation of the ellipse with center at (4, 2), major axis horizontal and of length 8 and with minor axis of length 6.

22. Find the area of the hexagon ABCDEF formed by joining the points A(1, 4), B(0, -3), C(2, 3), D(-1, 2), E(-2, -1) and F(3, 0).

23. The directrix of a parabola is the line y = 5 and its focus is at the point (4, -3). What is the length of its latus rectum?

24. Find the eccentricity of an ellipse when the length of the latus rectum is 2/3 of the length of the major axis.

25. Find the equation of the parabola whose axis is parallel to the x-axis and passes through the points (3, 1), (0, 0) and (8, -4).

26. A point P (x, 2) is equidistant from the points (-2, 9) and (4, -7). What is the value of x?

27. Find the equation of a line whose x-intercept is 2 and y-intercept is -2.

28. If the length of the latus rectum of an ellipse is three-fourth of the length of its minor axis, find its eccentricity.

Solutions to Problems #1-5

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