Question

Find the equation of the parabola which is symmetric about the $y$-axis and passes through the point $P(2,-3)$.

• A. $3y^2=4x$
• B. $3y^2=-4x$
• C. $y^2=-4x$
• D. $\text{None of these}$

Answer 1

The correct option is B $3y^2=-4x$

When the parabola is symmetrical about y-axis, its general equation is given by,

$x^2=4ay$ or $x^2=-4ay$

Now, point $P(2,-3)$ lies in forth quadrant and hence, parabola will open up downwards.

Thus, equation of parabola will be $x^2=-4ay$

Now, point P must satisfy equation of parabola as it lies on parabola.

$\therefore {\left(2\right)}^2=-4a(-3)$

$\therefore 4=12a$

$\therefore a=\frac{4}{12}$

$\therefore a=\frac{1}{3}$

Put this value in equation of parabola, we get,

$y^2=-4\left(\frac{1}{3}\right)x$

$\therefore y^2=\left(\frac{-4}{3}\right)x$

$\therefore 3y^2=-4x$