P is the point on the ellipse x216+y29=1 and Q is the corresponding point on the auxilliary circle of the ellipse. If the line joining centre C to Q meets the normal at P with repsect to the given ellipse at K, then the value of CK is
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Solution
Equation of normal at P is 4xcosθ−3ysinθ=7⋯(1)
Equation of auxiliary circle is x2+y2=16
Equation of normal at Q will be y=(tanθ)x⋯(2)
from (1) and (2) point of intersection will be K≡(h,k)≡(7cosθ,7sinθ) ∴CK=√72(sin2θ+cos2θ)=7 unit