ANALYTIC GEOMETRY
Points and Lines
1. Point P2 is located at (-3, 13). If point P1 has an abscissa of 3, determine its ordinate if the distance between
P1 and P2 is 10 units.
2. Determine the coordinates of the point which is 3/5 of the way from the point (-2, 5) to the point (-3, 5).
3. The segment from (-1, 4) to (2, -2) is extended three times its own length. What is the coordinates of the
terminal point?
4. Find the smallest angle between the line through (4, 4) and (-2, 0) and the line through (7, -1) and (-2, 5).
5. The vertices of a triangle are located at the following points: (-2, 0), (4, 0) and (3, 3). What is the area?
6. The vertices of a polygon are located at the following points: (-2, 7) (0, -8) (-4, -8) (3, 3) (-6, 0) (5, 0). What is
the area?
7. Find the equation of the locus of a point (x, y) for the following condition:
a. A point moves so that it produces constant inclination/slope of 3 and passes through (1, 1)
b. A point moves so that it is always equidistant from the points (-1, 0) and (3, 4)
c. A point moves so that it is always equidistant from the point (2, 1) and a vertical line x = 1.
8. Find the slope of the line 3x+4y-5=0 and its distance from the point (1, 2).
9. Find the distance between the parallel lines 4x-3y-12=0 and 4x-3y+8=0.
10. Find the equation of a line through point (3, 1) that is perpendicular to the line x+5y+5=0.
11. Find the equation of a line lying on (-2, 3) and (-3, 5).
12. Determine the x-intercept and y-intercept of the line3x+4y-12=0.
13. Determine the normal angle and the directed distance ρ of the line 4x-3y-15=0.
Circle
14. Find the equation of the circle tangent to the line 3x+4y=15 and the center is at (-3, -4).
15. Given: 4x2+4y2-4x+24y-107=0. Find its center and circumference.
Parabola
16. Given: 3x2+2x-5y+7=0. Find the ff:
a. LR end points and length of the LR
b. Coordinate of the vertex and focus
c. Equation of the directrix
17. Determine the equation of the parabola with vertex (-2, 5) and equation of the directrix x+4=0.
Ellipse
18. Given: 4x2+9y2-64x+54y+301=0. Find the ff:
a. Eccentricity, length of the semi-minor axis, major axis, and LR.
b. End points of major and minor axis.
c. Coordinates of the center, foci and the equations of directrices.
19. The semi-major axis of an ellipse is 4 and its semi-minor axis is 3. What is the distance between the
directrices?
Hyperbola
20. Given: 16y2-9x2+36x+96y-36=0. Find the ff:
a. Eccentricity, length of the transverse axis, semi-conjugate axis, and LR.
b. Area of the rectangle on the axes of the hyperbola
c. Coordinates of the center, foci and vertices
d. Equations of the directrices and asymptotes
21. Find the equation of the hyperbola with vertices at (-4, 2) and (0, 2) and foci at (-5, 2) and (1, 2).
Polar Coordinate System
22. Find the polar equation of the circle, if its center is at (4, 0) and the radius is 4.
23. Given the polar equation r=5sinѲ. Determine the rectangular form of the equation.
24. What is the polar form of the equation 3x2+2y2=8?
25. What is the distance between the point (5, 30o) and (-8, -50o).