- #1

utkarshakash

Gold Member

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## Homework Statement

The tangent at any point P of a circle meets the tangent at a fixed point A in T, and T is joined to B, the other end of diameter through A. Prove that the locus of point of intersection of AP and BT is an ellipse whose eccentricity is [itex] 1/ \sqrt{2}[/itex]

## Homework Equations

## The Attempt at a Solution

The very first thing I do is assume the equation of a circle. The next thing is to write the equations for tangents and solve them to get T. But it is getting complicated as nothing is known to me. So there are a number of variables which can't be eliminated. Any other ideas?