Question

If the area of the quadrilateral formed by the tangents from the origin to the circle $x^2+y^2+6x-10y+c=0$ and radii corresponding to the point of contact is $15$ sq. units, then value(s) of $c$ can be

• A. $5$
• B. $9$
• C. $16$
• D. $25$

Answer 1

Answer: (B), (D)

$25$

$x^2+y^2+6x-10y+c=0$
For the given circle, radius $r=\sqrt{9+25-c}$
Now $(0,0)$ should lie outside the circle.
Hence $c>0$

Length of tangent from $(0,0)$ to the circle is $L=\sqrt{c}$
So, required area is $=L\cdot r$
$15=\sqrt{c}\times \sqrt{9+25-c}\Rightarrow c^2-34c+225=0\Rightarrow c=9,25$