Focus of parabola

**prasum** · December 17th 2011, 08:08 AM

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

**princeps** · December 17th 2011, 08:29 AM

Originally Posted by prasum

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

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

$a=\frac{1}{k} , b =0 , c=\frac{3}{k} , D=b^2-4ac$

**prasum** · December 20th 2011, 10:18 AM

can yu tell me what will be the value of k 2 ,4,6 or 3

**Siron** · December 20th 2011, 10:46 AM

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.

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