Which of the following is the equation for the graph shown?

graph of an ellipse on a coordinate plane going through 12 comma 0, negative 12 comma zero, approximately 0 comma 10, and approximately 0 comma negative 10 with points inside ellipse at negative 7 comma 0 and 7 comma 0, and lines x equals 144 sevenths and x equals negative 144 sevenths

a
x squared over 144 plus y squared over 95 equals 1
b
x squared over 144 minus y squared over 95 equals 1
c
x squared over 95 plus y squared over 144 equals 1
d
x squared over 95 minus y squared over 144 equals 1

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raphealnwobi raphealnwobi · Answer 1 · 2022-02-24T12:33:19+01:00

The standard equation of an ellipse is [tex]\frac{x^2}{144} +\frac{y^2}{95} =1[/tex]

The standard equation of an ellipse is given by:

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1[/tex]

Where (h, k) is the center of the ellipse, 2a is the length of the major axis and 2b is the length of the minor axis.

Given the center = (0, 0), a = 12, b = 9.75, hence:

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1\\\\\frac{(x-0)^2}{12^2} + \frac{(y-0)^2}{9.75^2} =1\\\\\frac{x^2}{144} + \frac{y^2}{95} =1[/tex]

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