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Two tangents to a parabola meet at an an...

Two tangents to a parabola meet at an angle of `45^(@)` , prove that the locus of their point of intersection is the curve
`y^(2) = 4ax = ( x + a) ^(2)`
If they meet at an angle of ` 60^(@)` ,prove that the locus is
`y^(2) - 3 x^(2) - 10 ax - 3a ^(2) = 0`

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