If 'r' be the radius of largest circle with centre (3, 0) that can be inscribed in the ellipse
9x 2 + 25y 2 = 225, then 
r is equal to
Text Solution
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(21)
Sol. Largest circle will be that circle which touches the ellipse at any point (5cos θ θ , 3sin θ θ )
⇒ ⇒ Line joining points (5cos θ θ , 3sin θ θ ) and (3, 0) will be perpendicular to tangent of ellipse at point
(5cos θ θ , 3sin θ θ )
so that 
or 
and 
so that point on ellipse is 
.
Hence radius of circle is 
.
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