Question

If the line $y = m x + c$be a tangent to the circle $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$ , then the point of contact is.

• A. $\left( \frac { - a ^ { 2 } } { c } , a ^ { 2 } \right)$
• B. $\left( \frac { a ^ { 2 } } { c } , \frac { - a ^ { 2 } m } { c } \right)$
• C. $\left( \frac { - a ^ { 2 } m } { c } , \frac { a ^ { 2 } } { c } \right)$
• D. $\left( \frac { - a ^ { 2 } c } { m } , \frac { a ^ { 2 } } { m } \right)$

Answer 1

Answer: (C)

$\left( \frac { - a ^ { 2 } m } { c } , \frac { a ^ { 2 } } { c } \right)$

Answer 2

Find points of intersection by simultaneously

solving for x and y from $y = m x + c$ and $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$

which comes out as $\left( - \frac { a ^ { 2 } m } { c } , \frac { a ^ { 2 } } { c } \right)$.