A tangent to the ellipse at any point meets the line at a point . Let be the image of in the line , then the circle whose extremities of a diameter are and passes through a fixed point. The fixed point is

A tangent to the ellipse at any point meets the line at a point . Let be the image of in the line , then the circle whose extremities of a diameter are and passes through a fixed point. The fixed point is

a)

(3, 0)

b)

(5, 0)

c)

(0, 0)

d)

(4, 0)

1 Answer

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Answer Key / Explanation : (c) -

(c)

Equation of the tangent to the ellipse at is

It meets the line at

Image of in the line is

Equation of the circle is

i.e.,

Each member of the family passes through the intersection of and i.e., the point