ANALYTIC GEOMETRY TEST
Solve these questions. Make Diagrams. Show your work.
A/ Points and Lines:
1) Triangle ABC has vertices at A (2, 7), B (0, 0), and C (5, 1):
(a) Find the length of AC.
(b) Find the midpoint coordinates of AB.
(c) Find the perpendicular distance from A to BC.
(d) Write the equation of the line AC.
(e) Find the x and y intercepts of AC.
(f) Find the slopes of AB, AC, and BC to determine if ABC is a right-angled triangle.
(g) Find P such that the ratio of AP to PB is 1: 2.
2) Write the equation of the line:
(a) through ( – 7, 1) and (2, – 6).
(b) with x-intercept of 5, parallel to – 3x + 4y – 17 = 0.
(c) through the y-intercept of 2x + 5y – 15 = 0, perpendicular to x – y + 3 = 0.
(d) through (– 2, 1), parallel to the y-axis.
(e) through the y-intercept of y = 2x – 7, parallel to the x-axis.
B/ Circles:
1) Write the equation of the circle:
(a) center (0, 0), radius = 6.
(b) center (–2, 3), passing through (1, – 1).
(c) with diameter endpoints at (– 5, 2) and (3, 6).
2) Find the center and radius of the circle:
| (a) x2 + y2 = 49 |
(b) x2 + y2 + 2x + 6y – 26 = 0 |
(c) x2 + y2 – 75 = 10y |
3) Write the equation of the tangent(s) to:
(a) x2 + y2 = 25 at the point (– 4, 3). (b) x2 + y2 + 4x – 2y – 20 = 0 at (1, 5)
(c) x2 + y2 + 4x – 2y – 20 = 0 from the point (3, – 6).
C/ Parabolas:
1) y = 3x2 – 12x + 16:
(a) write the equation in standard form y = a(x – h)2 + k.
(b) does this parabola open upwards or downwards?
(c) what are the coordinates of the vertex?
(d) state whether there is a maximum or minimum y-value.
(e) what is the maximum or minimum value for y?
(f) what is the equation of the axis of symmetry for this parabola?
(g) find the x and y intercepts for this parabola.
2) Find the x-intercepts for:
(a) y = x2 – 6x – 7 (b) y = 2x2 + x – 15 (c) y = – x2 – x + 3
D/ Graphing:
1) y = – x2 + x + 6:
(a) put the equation in standard form y = a(x – h)2 + k.
(b) graph the parabola and label the vertex, x-intercepts and y-intercepts.
2) Solve graphically for the intersection point(s) of:
(a) the line y = 2x + 3 and the line y = – ½ x + 8.
(b) the circle (x – 3)2 + (y – 2)2 = 4 and the line y = – x + 3.
(c) the parabola y = x2 – 3x – 4 and the line y = – x – 1.
Analytic Geometry MathRoom Index
