Q.Find the equation of the locus of the point of intersection of perpendicular tangents drawn to the circle $x=5\cos\theta$, $y=5\sin\theta$.

The circle $x=5\cos\theta,\ y=5\sin\theta$ is $x^2+y^2=25$ in Cartesian form ($r=5$). The locus of the point of intersection of perpendicular tangents to a circle $x^2+y^2=a^2$ is its director circle, $x^2 …

Recognise the parametric equations as the circle $x^2+y^2=25$, then apply the dir …

• Forgetting to convert the parametric form to Cartesian first, and instead trying to apply the director-circle idea to $\theta$ directly …