Question

The length of the double ordinate of the parabola $y^2-8x+6y+1=0$ which is at a distance of $32$ units from vertex is

• A. $28$
• B. $30$
• C. $32$
• D. $26$

Answer 1

The correct option is C $32$

Given equation:$y^2-8x+6y+1=0$

$\Rightarrow$$(y+3{)}^2=8(x+1)$

$\Rightarrow$$y^2=8x$

This can be written as $y^2=4\times 2x$

Compairing with $y^2=4ax$

$\therefore$ $a=2$

$\Rightarrow$$a{t}^2=32$

$\Rightarrow$$t=4$

$\Rightarrow$length of double ordinate $=4at$

$=4\times 2\times 4$

$=32$