Question

P is the point on the ellipse is`x^2/16+y^2/9=1 and Q` is the corresponding point on the auxiliary circle of the ellipse. If the line joining the center C to Q meets the normal at P with respect to the given ellipse at K, then find the value of CK.

Answer 1

Equation of normal to ellipse
`(x^(2))/(16)+(y^(2))/(9)=1` at `P(4cos theta, 3 sin theta) ` is `(4x)/(cos theta)-(3y)/(sin theta)=7`
Normal passes through R(h,k)
`:. 4(h)/(cos theta)-3(k)/(sin theta)=7`
`rArr 4CR-3CR=7`
`rArrCR=7`