- #1

utkarshakash

Gold Member

- 855

- 13

## Homework Statement

If abscissa and ordinate of vertex of parabola [itex]y^2+2ax+2by-1=0[/itex] are equal then least possible length of latus rectum is

## Homework Equations

## The Attempt at a Solution

The give equation can be rewritten as

[itex]\left( y+b \right) ^2 = -2a\left\{ x-\dfrac{1+b^2}{2a} \right\}[/itex]

As given in question

[itex]-b=\dfrac{1+b^2}{2a} \\

1+b^2+2ab=0[/itex]

Length of latus rectum = a/2

But what can be the range of values of a?