Let from a point A (h, k) chords of contact are drawn to the...

Let the chord of contact is $PQ$ which touches $x^{2} + 4y^{2} = 4$ at $R$
Now, assume R = \left(2cos\theta,$2sin$\theta\right)
Equation$of the chord of contact PQ$ is $hx + 2yk = 6 \ldots . . \left(i\right)$
Again, the equation of the tangent $PQ$ is $\dfrac{xcos \theta}{2} + \dfrac{ysin \theta}{1} = 1 \ldots . . \left(ii\right)<br />From \left(i\right) and \left(ii\right), we get,</p><p> \dfrac{h2}{cos \theta} = \dfrac{2k}{sin\theta} =$6$<br />$cos \theta = $\dfrac{h}{3},$ sin \theta = $\dfrac{k}{3}⇒ x^{2} + y^{2} = 9</p><p>Hence, the$perimeter of the circle is 6\pi& units</p>