If the straight line `xcosalpha+ysinalpha=p` touches the curve `(x^2)/(a^2)+(y^2)/(b^2)=1` , then prove that `a^2cos^2alpha+b^2sin^2alpha=p^2dot`

Explanation

Given,
`x \cos \alpha+y \sin \alpha=p ` ....(i)


and the curve `x^{2} / a^{2}+y^{2} / b^{2}=1`



Also slope of line (i) is `-\frac{\cos \alpha}{\sin \alpha}`


...