Question

The equation of the directrix of a parabola $2x^2=14y$ is equal to

• A. $y=\frac{-7}{4}$
• B. $x=\frac{-7}{4}$
• C. $y=\frac{7}{4}$
• D. $x=\frac{7}{4}$

Answer 1

The correct option is A

$y=\frac{-7}{4}$

Find the equation of directrix

Given: Equation of the parabola is $2x^2=14y$

$\Rightarrow$ $x^2=7y$

Comparing $x^2=7y$ with the equation of a parabola ${\mathit{x}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}\mathit{a}\mathit{y}$.

$\Rightarrow$ $4ay=7y$

$\Rightarrow$ $a=\frac{7}{4}$

Equation of directrix of a parabola is $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathit{a}$

$\therefore$equation of directrix of the given parabola is $\mathit{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\frac{\mathbf{7}}{\mathbf{4}}$

Hence, Option ‘A’ is Correct.