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  4. If one end of a focal chord AB of the parabola y2 = 8x is at A((1/2), -2), then the equation of the tangent to it at B is :

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Q. If one end of a focal chord AB of the parabola $y^2 = 8x$ is at $A\left(\frac{1}{2}, -2\right)$, then the equation of the tangent to it at B is :

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Solution:

$4t_{1} = -2 \Rightarrow t_{1} = -\frac{1}{2}, $
$t_{1}.t_{2} = -1$
$t_{2} = -\frac{1}{t_{1}}$
$\Rightarrow t_{2} = 2$
So coordinate of B is $\left(8, 8\right)$
$\therefore $ Equation of tangent at B is
$8y = 4\left(x + 8\right) \Rightarrow 2y = x + 8$

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