Let the curve $C$ be the mirror image of the parabola $y^{2} = 4 x$ with respect to the line $x + y + 4 = 0$ . If $A$ and $B$ are the points of intersection of $C$ with the line $y = - 5$ , then the distance between $A$ and $B$ is (units)

Open in App

Solution

Let us consider the image of the line $y = - 5$ in the line $x + y + 4 = 0$ . The image will be the line $x = 1$ .

The line $x = 1$ will intersect the parabola $y^{2} = 4 x$ at the points $(1, - 2)$ and $(1, 2)$ .
The mirror image of these points in the line $x + y + 4 = 0$ are the points $A$ and $B$ . The distance between $A B$ and its pre-image is the same.
Distance between $(1, - 2)$ and $(1, 2)$ .

$= \sqrt{(1 - 1)^{2} + (2 + 2)^{2}} = 4$

Hence, distance $A B = 4$

Suggest Corrections

Similar questions

Let the curve $C$ be the mirror image of the parabola $y^{2} = 4 x$ with respect to the line $x + y + 4 = 0$ . If $A$ and $B$ are the points of intersection of $C$ with the line $y = - 5$ , then the distance between $A$ and $B$ is___

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

P (2, 1)

is :

Q. The line

x - y = 1

intersects the parabola

y^{2} = 4 x

A

and

B

. Normals at

A

and

B

intersect at

C

. If

D

is the point at which line

C D

is normal to the parabola, then coordinates of

D

are

The image of the point P(3, 5) with respect to the line y = x is the point Q and the image of Q with respect to the line y = 0 is the point R(a, b), then (a, b) =

Q. A straight line cuts the