Given the directrix of y = 6 and focus of (0, 4), which is the equation of the parabola?\

Mathematics

1 answer:

Yuliya22 [10]3 years ago

5 0

Answer:

The directrix is y=6 and focus is (0,4)

The equation of the parabola is,

20-4y=x²

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Recall what the cosecant function represents. It is the reciprocal of a sine function, and is often written in this form:

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$cosec(2sin^{-1}(\frac{-12}{13})) = \frac{1}{sin(2sin^{-1}(\frac{-12}{13}))}$

Let $u = sin^{-1}(\frac{-12}{13})$
$cosec(2sin^{-1}(\frac{-12}{13})) = \frac{1}{sin(2u)}$
$= \frac{1}{2sinu \cdot cosu}$
$= \frac{1}{2sin(sin^{-1}(\frac{-12}{13})) \cdot cos(sin^{-1}(\frac{-12}{13}))}$
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$= -\frac{13}{24} \cdot \frac{1}{\sqrt{\frac{25}{169}}}$
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