Question

The slope '$m$' of a tangent through the point $(7,1)$ to the circle $x^2+y^2=25$ satisfies the equation

• A. $12m^2+7m-12=0$
• B. $16m^2-24m+9=0$
• C. $12m^2-7m-12=0$
• D. $9m^2+24m+16=0$

Answer 1

The correct option is C $12m^2-7m-12=0$

Equation of the line passing through $(7,1)$ is

$(y-1)=m(x-7)$

$\therefore 5=\left|\frac{7m-1}{\sqrt{1+m^2}}\right|$

$\Rightarrow 25(1+m^2)=(7m-1{)}^2$

$\Rightarrow 25m^2+25=49m^2-14m+1$

$\Rightarrow 24m^2-14m-24=0$

$\Rightarrow 12m^2-7m-12=0$