# Focus of parabola

• Dec 17th 2011, 09:08 AM
prasum
Focus of parabola
x^2-ky+3=0 represents a parabola whose focus is in (0,2) find k
• Dec 17th 2011, 09:29 AM
princeps
Re: parabola
Quote:

Originally Posted by prasum
x^2-ky+3=0 represents a parabola whose focus is in (0,2) find k

$T\left(\frac{-b}{2a},\frac{-D}{4a}\right)=(0,2)$

$a=\frac{1}{k} , b =0 , c=\frac{3}{k} , D=b^2-4ac$
• Dec 20th 2011, 11:18 AM
prasum
Re: parabola
can yu tell me what will be the value of k 2 ,4,6 or 3
• Dec 20th 2011, 11:46 AM
Siron
Re: parabola
What have you tried? Princeps post tell's what you have to do, namely:
The equation of the parabola is:
$y=\frac{x^2+3}{k}$
Therefore we can find $k$ by solving the equation:
$\frac{-D}{4a}=2 \Rightarrow \frac{4ac-b^2}{4a}=2$

Proceed.