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