If 'P' be a moving point on the ellipse 
+ 
= 1 in such a way that tangent at 'P' intersect x = 
at Q then circle on PQ as diameter passes through a fixed point. Find that fixed point.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(3, 0)
Sol. 
+ 
=1 ...(1)
∴ e = 
= 
Equation of directrix : x = 
= 
= 
...(2)
Let a point P(5 cos θ , 4 sin θ ) on (1)
tangent at 'P' : 
cos θ + 
sin θ = 1 ...(3)
given that (3) cuts (2) (directrix) at Q
∴ By property we know that circle taking PQ as diameter,
always passes through corresponding focus
(ae, 0) ≡ 
≡ (3, 0)
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