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  4. The equation of the tangent to the parabola y2 = 8x which is parallel to the line 2x - y + 7 = 0, will be

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Q. The equation of the tangent to the parabola $y^2 = 8x$ which is parallel to the line $2x - y + 7 = 0, $ will be

Conic Sections

Solution:

The equation of any tangent to the parabola $y^{2} = 8x$ is
$ y=mx+\frac{2}{m} $
which is parallel to $2x-y+7=0$
whose slope $m=2$
On putting $m=2$ in $\left(1\right)$, we get
$ y=2x+1 $