Question

If a parabola having horizontal axis and passes through the points $(-2,1),(1,2)$ and $(-1,3)$ then the $y$-coordinate of the focus of that parabola is

• A. $\frac{37}{40}$
• B. $\frac{21}{10}$
• C. $\frac{41}{40}$
• D. $\frac{-41}{40}$

Answer 1

Answer: (B)

Equation of parabola $\Rightarrow y^2+A y+B x+C=0$
Passes through $(-2,1)(1,2)$ and $(-1,3)$
$y^2+A y+B x+C=0$
$\text { At }(-2,1) \Rightarrow 1+A-2 B+C=0$
$ \text { At }(1,2) \Rightarrow 4+2 A+B+C=0 $
$ \text { At }(-1,3) \Rightarrow 9+3 A-B+C=0$
$3+A+3 B=0$
$5+A-2 B=0$
$B=\frac{2}{5} A=-\frac{21}{5}$ and $C=4$
$ y^2-\frac{21}{5} y+\frac{2 x}{5}+4=0$
$\left(y-\frac{21}{10}\right)^2+\left(\frac{2}{5}\right) x+(4)=0$
As, $y$ coordinate of focus will be same as $y$ coordinate of vertex.
$\therefore \frac{21}{10}$