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Tangents are drawn from a point P on the...

Tangents are drawn from a point `P` on the curve `x^2 - 4y^2 = 4` to the curve `x^2 + 4y^2 = 4` touching it in the points `Q and R`. Show that the locus of the mid point of `QR` is `x^2/4 - y^2 = (x^2/4 + y^2)^2`.

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