Choose the correct answer. If the focus of a parabola is (0, -3) … - Vidyadip

MCQ

Choose the correct answer. If the focus of a parabola is (0, -3) and its directrix is y = 3, then its equation is:

✓
$x^2=-12 y$
B
$x^2=12 y$
C
$y^2=-12 x$
D
$y^2=12 x$

✓

Answer

Correct option: A.

$x^2=-12 y$

$x^2=-12 y$

Solution:
According to the definition of parabola,
$\sqrt{(\text{x}-0)^2+(\text{y}+3)^2}=\Bigg|\frac{\text{y}-3}{\sqrt{(0)^2+(1)^2}}\Bigg|$
$\Rightarrow\sqrt{\text{x}^2+\text{y}^2+9+6\text{y}}=|\text{y}-3|$
Squaring both sides, we get
$x^2+y^2+9+6 y=y^2+9-6 y$
$\Rightarrow x^2+9+6 y=9-6 y$
$\Rightarrow x^2=-12 y$

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