some math questions on analytic geometry
some math questions on analytic geometry
2. Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3.
8. Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 10.
9. Find the vertices and foci of the hyperbola with equation 
= 1.
10. Graph the hyperbola with equation 
= 1.
11. Find an equation in standard form for the hyperbola with vertices at (0, ±6) and foci at (0, ±9).
12. Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ± 
x.
13. Eliminate the parameter.x = 
t, y = 3t3 – 1
14. Find the rectangular coordinates of the point with the polar coordinates. 
15. Find all polar coordinates of point P where P = 
.
16. Determine two pairs of polar coordinates for the point (5, 5) with 0° ≤ θ < 360°.
17. The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph.
[-5, 5] by [-5, 5]
18. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 + 3 sin θ
19. A railroad tunnel is shaped like a semiellipse, as shown below.
The height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. Find an equation for the ellipse.
20. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 3θ
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