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Equation of Tangent When a Point Is Given

The equation ...

Question

The equation of tangent to the parabola $y^{2} = x$ at point $(4, 2)$ is

4 y + x + 12 = 0

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2 y - 3 x + 8 = 0

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2 y + x - 8 = 0

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4 y - x - 4 = 0

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Solution

The correct option is D $4 y - x - 4 = 0$
Given parabola
$y^{2} = x$
The equation of tangent at $(4, 2)$ is
$T = 0 2 \cdot y = \frac{(x + 4)}{2} \Rightarrow 4 y = (x + 4) \Rightarrow 4 y - x - 4 = 0$

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y^{2} = x

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y^{2} = 9 x

(4, 10)

If the tangent at the point P(2, 4) to the parabola $y^{2} = 8 x$ meets the parabola $y^{2} = 8 x + 5$ at Q and R,
then the midpoint of QR is

P_{1} : y^{2} = 4 a x, P_{2} : y^{2} = - 4 a x L : y = x

P_{1}

L

x^{2} + y^{2} - 4 x - 4 y + 4 = 0

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