Question

What is the equation of the parabola that has a vertex at `(21, 11)` and passes through point `(23,-4)`?

Answer 1

`2(y-11)^2=225(x-21)` (Parabola opened rightwards,(i.e,)towards positive x direction)

Explanation:

The General equation of a parabola is `(y-k)^2=4a(x-h)`

(Parabola opened towards positive x-direction)

where

`a` is a arbitrary constant,

( `h,k`) is the vertex.

Here we have our vertex as ( `21,11`).

SUBSTITUTE the x and y coordinate values of the vertex in the equation above, we get.

`(y-11)^2=4a(x-21)`

In order to find the value of ' `a`' substitute the given point in the equation

then we get

`(-4-11)^2=4a(23-21)`
`=>(-15)^2=8a`

`=>a=225/8`

Substitute the value for ' `a`' In the above equation to have the equation of the required parabola.

`(y-11)^2=4*225/8(x-21)`
`=>2(y-11)^2=225(x-21)`

`color(blue)(NOTE):`

The general equation of a parabola "OPENED UPWARDS " will

results in a slightly different equation , And leads to a different

answer . Its general form will be

`(x-h)^2=4*a(y-k)`

where (h,k) is the vertex..,