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Let the curve C be the mirror image of the parabola y^{2}=4x with respect to the line x+y+8=0 . If A and B are the points of intersection of C with the line y=-4 , then the distance between A and B is : 

Option: 1

12


Option: 2

16


Option: 3

10


Option: 4

14


Answers (1)

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Consider the image of the line y=-4 in the line x+y+8=0 .

To find the image line put the value of y in the equation x+y+8=0

\begin{aligned} & \Rightarrow x-4+8=0 \\ & \Rightarrow x=4 \end{aligned}
The image will be the line x=4.

Find intersection point of line x=4 and y^{2}=4x

put x=4  in y^{2}=4x .

we get y=(4,-4)

So the line x=4 will intersect the parabola y^{2}=4x at the points (4,-4)and  (4,4).

Let the mirror image of these points in the line x+y+8=0 are points A and B.

The distance between AB and its pre-image is the same.

Find distance between (4,-4) and  (4,4) using the distance formula.

\mathrm{AB}=\sqrt{\left(256^2+0\right)}=16

Distance between A and B is 16 units.

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manish painkra

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