Mathematics: What is the equation of the ellipse with foci at (5, 0), (-5, 0) and vertices (9, 0), (-9, 0)?

What is the equation of the ellipse with foci

roadrnr5183

30.01.2022

$\dfrac{x^2}{81}+\dfrac{y^2}{56}=1$

Step-by-step explanation:

General equation of ellipse : $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}$

Given: Vertices of ellipse : (± 9,0)

Since the vertices are of the form (± a, 0).

i.e. a=9

Thus, the major axis is along x-axis.

Also, foci of the ellipse = (±5,0)

Since, foci is of the form (± c,0), i.e. c=5

Since

$c^2=a^2-b^2\\\\\Rightarrow\ 5^2= 9^2-b^2\\\\\Rightarrow\ b^2=81-25\\\\\Rightarrow\ b^2=56$

Equation of ellipse :

$\dfrac{x^2}{9^2}+\dfrac{y^2}{56}=1\\\\\Rightarrow\ \dfrac{x^2}{81}+\dfrac{y^2}{56}=1$

Hence, the required equation : $\dfrac{x^2}{81}+\dfrac{y^2}{56}=1$

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moynihansavanah003

21.10.2020

Tommy would have to pull at least 40.0000000 something to beat Artie but the closest whole number is 41 becouse it has to be over 200

Step-by-step explanation:

200 /= 60 + 20 +25 + 55 + x

200/= 160 + x - 160 both sides

40 = x

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