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Focal Distance

The parabola ...

Question

The parabola $x^{2} = p y$ passes through (12, 16). Then the focal distance of the point is

$\frac{57}{4}$

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$\frac{73}{4}$

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Solution

The correct option is B
$\frac{73}{4}$

$x^{2} = p y passes through (12, 16)$
$\Rightarrow 144 = p \times 16 \Rightarrow p = 9$
$x^{2} = 9 y$
$4 a = 9 \Rightarrow a = \frac{9}{4}$
$focal distance = | y_{1} + a | = | 16 + \frac{9}{4} | = \frac{73}{4}$

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Similar questions

The parabola $x^{2} = p y$ passes through (12, 16). Then the focal distance of the point is

A

(9, 12)

y^{2} = 16 x

B

x^{2} = p y

(12, 16)

C

y^{2} = k x

(9, 6)

k

D

y^{2} = 36 x

x^{2} + 4 y^{2} = 16

(4 cos θ, 2 sin θ)

x^{2} = 8 (y - 6)

x^{2} + 4 y^{2} = 16

O

x^{2} = 8 (y - 6)

θ

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