The curvature K of $x ^ { 2 } + y ^ { 2 } = 25$ at (-3, -4) is

A) $\frac { 2 } { 25 \sqrt { 5 } }$
B) $\frac { 1 } { 2 \sqrt { 2 } }$
C) $\frac { 2 } { 5 \sqrt { 5 } }$
D) $\frac { 2 } { 17 \sqrt { 17 } }$
E) $\frac { 1 } { 5 }$

Question

The curvature K of $x ^ { 2 } + y ^ { 2 } = 25$ at (-3, -4) is

A) $\frac { 2 } { 25 \sqrt { 5 } }$
B) $\frac { 1 } { 2 \sqrt { 2 } }$
C) $\frac { 2 } { 5 \sqrt { 5 } }$
D) $\frac { 2 } { 17 \sqrt { 17 } }$
E) $\frac { 1 } { 5 }$

Quizplus · Accepted Answer

The given equation is a circle with radius 5. The curvature of a circle is the reciprocal of its radius, so the curvature is $ \frac{1}{5} $.

The Curvature K Of x2+y2=25x ^ { 2 } + y ^ { 2 } = 25x2+y2=25

The Curvature K Of $x ^ { 2 } + y ^ { 2 } = 25$