The line `2x−y+4=0` cuts the parabola `y^2=8x` in `P and Q`. The mid-point of PQ is (a) `(1,2)` (b) `(1,-2)` (c) `(-1,2)` (d) `(-1,-2)`

Explanation

`(-1,2)`

Let the coordinates of P and Q be` (a t_{1}^{2}, 2 a t_{1})` and `(a t_{2}{ }^{2}, 2 a t_{2})` respectively. Slope of` P Q=frac{2 a t_{2}-2 a t_{1}}{a t_{2}^{2}-a t_{1}^{2}}`

But, the slope of P Q is equal to the slope of `2 x-y+4=0.`

therefore Slope of P Q=`frac{-2}{-1}=2`

From (1),` frac{2 a t_{2}-2 a t_{1}}{a t_{2}^{2}-a t_{1}^{2}}=2`
Putting `4 a=8`,


`a=2`

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