1.

Consider a hyperbola (y^(2))/(4)-(x^(2))/(4) = alpha, If the common tangent of the hyoerbola and parabola meets the coordinates axes at x and A and B, then locus of mid point of AB is

Answer»

`x^(2) = -2y`
`2x^(2) = -y`
`x^(2) = - 4y`
`(x^(2))/(2) - (y^(2))/(1) = -1`

Solution :Equation of the common tangent is `y = tx - t^(2)`
`:.` MID point of `AB` is `((L)/(2),(t^(2))/(2))`
`:.` the LOCUS is `y = -2x^(2)`


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