Question

The parabola $y^2=px$ passes through the point of intersection of lines $\frac{x}{3}+\frac{y}{2}=1$ and $\frac{x}{2}+\frac{y}{3}=1$ its focus is

• A. $(\frac{3}{10},0)$
• B. $(\frac{3}{5},0)$
• C. $(\frac{3}{7},0)$
• D. $(\frac{6}{7},0)$

Answer 1

The correct option is A $(\frac{3}{10},0)$

Point of intersection of $\frac{x}{3}+\frac{y}{2}=1,\frac{x}{2}+\frac{y}{3}=1$ will be
$=(\frac{6}{5},\frac{6}{5})$

This point passes through parabola $y^2=px$
$\Rightarrow {\left(\frac{6}{5}\right)}^2=p\left(\frac{6}{5}\right)$
$\Rightarrow p=\frac{6}{5}$

Focus of the parabola $y^2=4ax$ is given as $(a,0)$
$\therefore$ coordinate of focus will be $(\frac{p}{4},0)=(\frac{3}{10},0)$