Question

The equation of pair of tangents from origin to a circle is $24xy+7y^2=0$. If the radius of the circle is 3 , then the length of the tangent drawn from the origin is

• A. $7$
• B. $24$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

$24xy+7y^2=0$
$y(24x+7y)=0$
$y=0$ and $24x+7y=0$, this are two tangents from origin to circle
${\perp }^{ar}$ distance of $y=0$ from $C(h,k)$ is 3
$\Rightarrow 3=\left|\frac{k}{1}\right|$
$\Rightarrow k=-3$
Also, ${\perp }^{ar}$ distance of $24x+7y=0$ from $c(h,k)$ is 3
$\Rightarrow 3=\left|\frac{24h+7k}{25}\right|$
$\Rightarrow 75=|24h+7k|$
$\Rightarrow 75+21=24h$
$\Rightarrow h=\frac{96}{24}=4$
So, length of tangent from $C(4,-3)$
$=\sqrt{(CO{)}^2-(CA{)}^2}$
$=\sqrt{25-9}$
$=4$