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If the vertex of a parabola is the point...

If the vertex of a parabola is the point `(-3,0)` and the directrix is the line `x+5=0`, then find its equation.

A

`y^(2)=8(x+3)`

B

`x^(2)=8(y+3)`

C

`y^(2)=-8(x+3)`

D

`y^(2)=8(x+5)`

Text Solution

Verified by Experts

The correct Answer is:
A
Here, vertex=(-3,0)
`therefore`a=-3 and directrix,x+5=0

Since, axis of the parabola is a line perpendicular to directrix and A is the midpoint of AS
Then `-3=(x_(1)-5)/2`
`rArr-6=x_(1)-5rArrx_(1)=-1`
`0=(0+y_(1))/2rArry_(1)=0`
`thereforeS=(-1,0)`
`because`PM=PS
`rArr abs(x+5)=sqrt((x+1)^(2)+y^(2))`
`rArr x^(2)+2x+1+y^(2)=x^(2)+10x+25`
`rArr y^(2)=+8x+24`
`rArry^(2)=+8(x+3)`
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