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  • is a normal to the parabola <img alt="y^2=4 a x" src="https://entrancecorner.onc

y=-2 x+12 a is a normal to the parabola y^2=4 a x at the point whose distance from the focus of the parabola is .......

Option: 1

0


Option: 2

a


Option: 3

5a


Option: 4

2a


Answers (1)

best_answer

We know y=m x-2 a m-a m^3 is a normal to the parabola y^2=4 a x at the point \left(\mathrm{am}^2,-2 a m\right)

The given equation can be written as

                  y=-2 x-2 a(-2)-(-2)^3 a

which represents a normal to the parabola corresponding to m=-2 at the point (4 a, 4 a) whose distance from the focus (a, 0) is

           \sqrt{(4 a-a)^2+(4 a)^2}=\sqrt{\left(9 a^2+16 a^2\right)}=5 a        

Posted by

Anam Khan

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