### Home > PC3 > Chapter 10 > Lesson 10.1.4 > Problem10-85

10-85.

Graph each equation below. Also include all of the key information, such as the locations of the foci and/or the equations of any asymptotes.

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

Since the terms are both squared, being added, and the equation is equal to $1$, this is an ellipse.

The center is at $(1, 0)$. The 'horizontal radius' = 3 and the 'vertical radius' $= 2$.

1. $(x − 4)^2 + (y + 2)^2 = 25$

This equation has the form $(x − h)^2 + (y − k)^2 = r^2$, so this is a circle.

1. $\frac { ( y - 2 ) ^ { 2 } } { 36 } - \frac { ( x - 3 ) ^ { 2 } } { 9 }= 1$

The terms are both squared, being subtracted, and the $y$-term is positive.

This is a hyperbola that is vertically oriented.

1. $5x + (y − 2)^2 = 20$

When you isolate the $x$-term, the equation becomes:

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

This is a parabola that opens to the left.