Writing the Equations of Conic Sections

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

• $\left(x-2\right)^2=-12\left(y+5\right)$

• $\left(x+2\right)^2=-12\left(y-5\right)$

• $\left(x-2\right)^2=12\left(y+5\right)$

• $\left(x+2\right)^2=12\left(y-5\right)$

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

•  $\left(y-2\right)^2=8\left(x+1\right)$  

•  $\left(y+2\right)^2=8\left(x-1\right)$  

•  $\left(x+1\right)^2=8\left(y-2\right)$  

•  $\left(x-1\right)^2=8\left(y+2\right)$  

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

• $\left(x+2\right)^2+\left(y-3\right)^2=4$

• $\left(x-2\right)^2+\left(y-3\right)^2=4$

• $\left(x+2\right)^2+\left(y-3\right)^2=16$

• $\left(x-2\right)^2+\left(y+3\right)^2=16$

Find the center of the circle  $x^2-2x+y^2+10y+17=0$  

• (5,-1)

• (-5,1)

• (1,-5)

• (-1,5)

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

• $\frac{\left(x+1\right)^2}{9}+\frac{\left(y+2\right)^2}{4}=1$

• $\frac{\left(x+1\right)^2}{4}+\frac{\left(y+2\right)^2}{9}=1$

• $\frac{\left(x+1\right)^2}{9}-\frac{\left(y+2\right)^2}{4}=1$

• $\frac{\left(x+1\right)^2}{4}-\frac{\left(y+2\right)^2}{9}=1$

Write the equation of an ellipse with foci (-5,2) and (3,2) and minor axis endpoints (-1,5) and (-1,-1)

• $\frac{\left(x+1\right)^2}{9}+\frac{\left(y-2\right)^2}{16}=1$

• $\frac{\left(x+1\right)^2}{16}+\frac{\left(y-2\right)^2}{9}=1$

• $\frac{\left(x+1\right)^2}{9}+\frac{\left(y-2\right)^2}{25}=1$

• $\frac{\left(x+1\right)^2}{25}+\frac{\left(y-2\right)^2}{9}=1$

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

• $\frac{\left(y+1\right)^2}{4}-\frac{\left(x+3\right)^2}{9}=1$

• $\frac{\left(x+3\right)^2}{9}-\frac{\left(y+1\right)^2}{4}=1$

• $\frac{\left(y+1\right)^2}{9}-\frac{\left(x+3\right)^2}{4}=1$

• $\frac{\left(x+3\right)^2}{4}-\frac{\left(y+1\right)^2}{9}=1$

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

• $\frac{\left(y+5\right)^2}{25}-\frac{\left(x-2\right)^2}{11}=1$

• $\frac{\left(y+5\right)^2}{11}-\frac{\left(x-2\right)^2}{25}=1$

• $\frac{\left(x-2\right)^2}{11}-\frac{\left(y+5\right)^2}{25}=1$

• $\frac{\left(x-2\right)^2}{25}-\frac{\left(y+5\right)^2}{11}=1$

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

•  $a>b$  

•  $a$  is the horizontal distance from the center to a point on the ellipse.

•  $a$  is the vertical distance from the center to a point on the ellipse.

•  $a^2+b^2=c^2$  

•  $a^2-b^2=c^2$  

Which of the following are always true for a hyperbola (mark all correct answers)

•  $a>b$  

•  $a$  is the horizontal distance from the center to a point on the hyperbola.

•  $a$  is the vertical distance from the center to a point on the hyperbola.

•  $a^2+b^2=c^2$  

•  $a^2-b^2=c^2$