4(x² − 6x + 9) − (y² + 10y + 25) = 5 + 36 − 25

4(x − 3)² − (y + 5)² = 16

$\frac{(x-3)^2}{4}-\frac{(y+5)^2}{16}=1$

This is a hyperbola.

See part (a).

(x + 5)² + (y − 2)² = 16
This is a circle.

See part (a).

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

This is an ellipse.

Set the equation equal to y and complete the square for x.

y = 3(x − 2)² + 5
This is a parabola.