Question

Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (11, 0) and an eccentricity of three fifths question mark

quantity x minus 6 end quantity squared over 100 plus y squared over 64 equals 1
quantity x plus 6 end quantity squared over 64 plus y squared over 100 equals 1
quantity x plus 6 end quantity squared over 16 plus y squared over 25 equals 1
quantity x minus 6 end quantity squared over 25 plus y squared over 16 equals 1

Answer 1

The equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.

What is an ellipse?

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

The vertices of the ellipse = (1, 0) and (11, 0)

Eccentricity of ellipse = 3/5

We have equations:

$\rm \dfrac{\left(x-6\right)^{2}}{100}+\dfrac{y^{2}}{64}=1$

$\rm \dfrac{\left(x+6\right)^{2}}{64}+\dfrac{y^{2}}{100}=1$
$\rm \dfrac{\left(x+6\right)^{2}}{16}+\dfrac{y^{2}}{25}=1$

$\rm \dfrac{\left(x-6\right)^{2}}{25}+\dfrac{y^{2}}{16}=1$

From the fourth equation:

The vertices of the ellipse:

(1, 0) and (11, 0)

The eccentricity:

c²  = a² - b²

c² = 25-16

c = 3

e = c/a = 3/5

Thus, the equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.

Learn more about the ellipse here:

https://brainly.com/question/19507943

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