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  • Axis of a parabola lies along the   . If its vertex and focus are at distances <img alt="2" src=

Axis of a parabola lies along the  X-axis . If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive X-axis, then which of the following points does not lie on it?

Option: 1

(4,-4)


Option: 2

(6,4 \sqrt{2})


Option: 3

(8,6)


Option: 4

(5,2 \sqrt{6})


Answers (1)

best_answer

According to given information, we have the following figure

Now, if the origin is shifted to  (2,0)   and  (X,Y)  are the coordinates with respect to new origin, then the axis of the parabola lies along the x-axis, the equation of the parabola can be written as:

 Y^{2}=4aX

 where a is the distance from the vertex to the focus, and x is the distance from the vertex to any point on the parabola.

 , X=x-2

And

  Y=y

and a=4-2\\\therefore y^{2}=8(x-2)

And, (8, 6) is the only point which does not satisfy the equation.

 

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mansi

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