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Circles are drawn with their centres on ...

Circles are drawn with their centres on the axis of `x` and touching the straight line `y=x tan alpha`. Show that the points of contact of the tangents from a fixed point `(h, k)` will lie on the curve given by : `(x-h)^2 (y^2 - x^2 sin^2 alpha) - 2xy (x-h) (y-k) sin^2 alpha + y^2 (y-k)^2 cos^2 alpha = 0`.

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