Find the condition on kkk such that the line xcosα+ysinα=px \cos \alpha + y \sin \alpha = pxcosα+ysinα=p is a normal to the hyperbola x2a2−y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1a2x2−b2y2=1.
a2cos2α−b2sin2α=(a2+b2)2p2\frac{a^2}{\cos^2 \alpha} - \frac{b^2}{\sin^2 \alpha} = \frac{(a^2+b^2)^2}{p^2}cos2αa2−sin2αb2=p2(a2+b2)2
a2cos2α+b2sin2α=p2\frac{a^2}{\cos^2 \alpha} + \frac{b^2}{\sin^2 \alpha} = p^2cos2αa2+sin2αb2=p2
a2cos2α−b2sin2α=p2a^2 \cos^2 \alpha - b^2 \sin^2 \alpha = p^2a2cos2α−b2sin2α=p2
a2cos2α−b2sin2α=p2\frac{a^2}{\cos^2 \alpha} - \frac{b^2}{\sin^2 \alpha} = p^2cos2αa2−sin2αb2=p2