Equations of Conic Sections

What is the center and radius of the curve:

x= -1 + 9cost

y= 2 + 9sint

• (-1,2) , r=3

• (-1,2) ,  r=9

• (1,-2) ,  r=3

• (1,-2) ,  r=9

Write the equation of a parabola with a vertex at (-2,5), that opens down, and has a focal width of 12.

Write the equation of a parabola with a focus at (1,2) and a directrix of x=-3

Write the equation of a circle with a center at (2,-3) and a radius of 4.

Write the equation of an ellipse with major axis endpoints of (-1,1) and (-1,-5) and a minor axis length of 4.

Write the equation of a hyperbola with conjugate axis endpoints (-6,-1) and (0,-1) and a transverse axis length of 4.

Write the equation of a hyperbola with foci (-4,-5) and (8,-5) and a transverse axis length of 10.

Which of the following are always true for an ellipse (mark all correct answers)

• Circle

• Parabola

• Ellipse

• Hyperbola