Question

For the parabola $x^2+7y=0,$ which of the following is/are correct ?

• A. Equation of directrix is $4y-7=0$
• B. Focus of the parabola is $(0,\frac{7}{4})$
• C. Length of latus-rectum is $7$ units.
• D. End points of latus-rectum are $(-\frac{7}{2},-\frac{7}{4})$ and $(-\frac{7}{2},\frac{7}{4})$

Answer 1

Answer: (A), (C)

Length of latus-rectum is $7$ units.


$x^2=-7y$
Since it is a downward opening parabola, it is of form $x^2=-4ay$
$\Rightarrow 4a=7$
$\Rightarrow a=\frac{7}{4}$
Equation of directrix $y=a$
$\therefore$ Equation of directrix is $4y-7=0$
End of latus-rectum $(2a,-a)$ and $(-2a,-a)$
i.e. $(\frac{7}{2},-\frac{7}{4})$ and $(-\frac{7}{2},-\frac{7}{4})$