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tabita57i

Answered question

2021-08-11

Find the vertices and foci of the conic section. $\frac{x^{2}}{4} - \frac{y^{2}}{9} = 36$

Answer & Explanation

Maciej Morrow

Skilled2021-08-12Added 98 answers

The conic section has solution:

Vasquez

Expert2021-12-27Added 669 answers

Step 1

To find the vertices and foci of the conic section.

Given the equation,

$\frac{x^{2}}{4} - \frac{y^{2}}{9} = 36$

1) $\frac{x^{2}}{144} - \frac{y^{2}}{324} = 1$

Hence, the given equation is form of hyperbola.

Here,

$a^{2} = 144 \Rightarrow a = 12$

$b^{2} = 324 \Rightarrow b = 18$

Step 2

equation (1) compare this below equation

$\frac{(x - h)^{2}}{a^{2}} - \frac{(y - k)^{2}}{b^{2}} = 1$

$c^{2} = a^{2} + b^{2}$

$c = \sqrt{a^{2} + b^{2}}$

$c = \sqrt{144 + 324}$

$c = \sqrt{468}$

Vertices of hyperbola $= (h, k) = (0, 0)$

Foci of hyperbola $= (\pm c, 0) = (\pm \sqrt{468}, 0)$

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