### Home > APCALC > Chapter 8 > Lesson 8.3.3 > Problem8-128

8-128.

Multiple Choice: If $x^2 + y^2 = 25$ then $\frac { d ^ { 2 } y } { d x ^ { 2 } }=$

1. $- \frac { x } { y }$

1. $\frac { x + y } { y ^ { 2 } }$

1. $- \frac { 25 } { y ^ { 3 } }$

1. $\frac { x ^ { 2 } - y ^ { 2 } } { y ^ { 3 } }$

1. $\frac { y ^ { 2 } - x } { y ^ { 3 } }$

$\frac{d}{dx}(x^{2}+y^{2})=\frac{d}{dx}25$

$\frac{dy}{dx}=\frac{-x}{y}$

$\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left (\frac{-x}{y} \right )$

$\frac{d^{2}y}{dx^{2}}=\frac{-(y^{2}+x^{2})}{y^{3}}$

Uh-oh! None of the multiple choice options match! That does not mean you are wrong. Look at the original equation of the circle.
What does $x^2 + y^2$ equal? Substitute that value and find your solution.