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Let C be the ...

Question

Let $C$ be the locus of the mirror image of a point on the parabola $y^{2} = 4 x$ with respect to the line $y = x .$ Then the equation of tangent to $C$ at $P (2, 1)$ is :

2 x + y = 5

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x + 2 y = 4

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x + 3 y = 5

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x - y = 1

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Solution

The correct option is D $x - y = 1$

Image of $y^{2} = 4 x$ w.r.t. $y = x$ is $x^{2} = 4 y$
Tangent from $(2, 1)$ is $T = 0$
$x x_{1} = 2 (y + y_{1})$
$\Rightarrow 2 x = 2 (y + 1)$
$\Rightarrow x = y + 1$

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Let C be the locus of the mirror image of a point on the parabola y2=4x with respect to the line y=x. Then the equation of tangent to C at P(2,1) is :

The correct option is D x−y=1 Image of y2=4x w.r.t. y=x is x2=4y Tangent from (2,1) is T=0 xx1=2(y+y1) ⇒2x=2(y+1) ⇒x=y+1

Let $C$ be the locus of the mirror image of a point on the parabola $y^{2} = 4 x$ with respect to the line $y = x .$ Then the equation of tangent to $C$ at $P (2, 1)$ is :

The correct option is D $x - y = 1$

Image of $y^{2} = 4 x$ w.r.t. $y = x$ is $x^{2} = 4 y$
Tangent from $(2, 1)$ is $T = 0$
$x x_{1} = 2 (y + y_{1})$
$\Rightarrow 2 x = 2 (y + 1)$
$\Rightarrow x = y + 1$