Find the vertices and foci of the conic section. x^2/4 − y^2/9 = 36

tabita57i 2021-08-11 Answered

Find the vertices and foci of the conic section. x24y29=36
image

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Expert Answer

Maciej Morrow
Answered 2021-08-12 Author has 98 answers
Vasquez
Answered 2021-12-27 Author has 460 answers

Step 1

To find the vertices and foci of the conic section.

Given the equation,

x24y29=36

1)\x2144y2324=1

Hence, the given equation is form of hyperbola.

Here,

a2=144a=12

b2=324b=18

Step 2

equation (1) compare this below equation

(xh)2a2(yk)2b2=1

c2=a2+b2

c=a2+b2

c=144+324

c=468

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

Foci of hyperbola =(±c,0)=(±468,0)

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