Maths-
General
Easy
Question
An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is
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- 2
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The correct answer is: 2
Focus = (3, 0)
Let the circle touches the ellipse at P and Q. Consider a tangent (to both circle and ellipse) at P. Let F(one focus) be the centre of the circle and other focus be G. A ray from F to P must retrace its path (normal to the circle). But the reflection propety the ray FP must be reflected along PG. This is possible only if P, F and G are collinear. Thus P must be the end of the major axis. Hence r = a – ae = 5 – 3 = 2 alternately normal to an ellipse at P must pass through the centre (3, 0) of the circle
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