# CBSE Class 11-science Answered

**Find the equation of the parabola with vertex [2,-3] and focus [0,5]**

Asked by arkabanerjee | 29 Jan, 2011, 09:05: PM

Expert Answer

Dear student,

Let A(2, -3) be the vertex and F(0, 5) be the focus.

Let the axis meet the directrix at a point Z(α,β).

Then, A is the mid point of ZF.

So, 2 = α+0/2

α=4

and, -3=β+5/2

β=-11

Thus, the coordinates of Z are (4, -11).

Now, slope of ZF = 5+11/0-4=-4

So, slope of the directrix = 1/4

Thus, the directrix is a line passing through the point (4, -11) and has a slope equal to 1/4.

Thus, the equation of the directrix is given by:

Let P (x, y) be any point on the parabola. Then,

PF = length of the perpendicular from P on x-4y-48=0

Simplify this expression to get the required equation of the parabola.

We hope that this clarifies your query.

Regards,

Team

TopperLearning

Answered by | 07 Feb, 2011, 09:46: PM

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