91Ó°ÊÓ

Writing. Describe the similarities and differences between hyperbolas and ellipses.

Find the vertices and the asymptotes of each hyperbola. $$ y^{2}-4 x^{2}=64 $$

Open-Ended Describe any other figures you can imagine that can be formed by the intersection of a plane and other shapes.

Use the given information to write an equation of the circle. center \((-2,7.5),\) circumference 3\(\pi\)

Error Analysis A student claims that an ellipse has vertices at \(( \pm 3,0)\) and co-vertices at \((0, \pm 7) .\) What is the student's error?

Open-Ended Find a real-world design that uses ellipses. Place a coordinate grid over the design and write an equation of the ellipse.

Sound An airplane flying faster than the speed of sound creates a cone-shaped pressure disturbance in the air. This is heard by people on the ground as a sonic boom. What is the shape of the path on the ground?

Use the given information to write an equation of the circle. translation of \((x-1)^{2}+(y+3)^{2}=36,2\) units left and 4 units down

Write an equation of an ellipse in standard form with center at the origin and with the given characteristics. vertex \((-11,0),\) co-vertex \((0,9)\)

Error Analysis A student claims that the circle \((x+7)^{2}+(y-7)^{2}=8\) is a translation of the circle \(x^{2}+y^{2}=8,7\) right and 7 down. What is the student's mistake?