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:

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: (A) x - y = 1 (B) 2 x + y = 5 (C) x + 3 y = 5 (D) x + 2 y = 4

Tardigrade Admin · Accepted Answer

Given y 2=4 x Mirror image on y = x ⇒ C: x 2=4 y 2 x =4 ⋅ ( d y / dx ) ⇒ ( dy / dx )=( x /2) .( dy / dx )| P (2,1)=(2/2)=1 Equation of tangent at (2,1) ⇒ y -1=1( x -2) ⇒ x-y=1

Q. 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:

x - y = 1

2 x + y = 5

x + 3 y = 5

x + 2 y = 4

Given $y^{2} = 4 x$
Mirror image on $y = x$
$\Rightarrow C : x^{2} = 4 y$
$2 x = 4 \cdot \frac{d y}{d x} \Rightarrow \frac{d y}{d x} = \frac{x}{2}$
$\frac{d y}{d x} ∣ ∣_{P (2, 1)} = \frac{2}{2} = 1$
Equation of tangent at $(2, 1)$
$\Rightarrow y - 1 = 1 (x - 2)$
$\Rightarrow x - y = 1$

Q. 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: