The center of an ellipse is (1,6). One focus of the ellipse is (−3,6). One vertex of the ellipse is (8,6). What is the equation of the ellipse in standard form?

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Step-by-step explanation:

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Step-by-step explanation:

We have been given that the center of an ellipse is (1,6). One focus of the ellipse is (-2,6). One vertex of the ellipse is (10,6).

We know that standard equation of an ellipse centered at (h,k) is in form:

, where,

a = Horizontal radius

b = Vertical radius.

Since center of the ellipse is at point (1,6) and one vertex is (10,6), so the horizontal radius would be 9 (10-1) units.

Now, we will find vertical radius using formula , where c represents focal length.

Substituting given values:

Upon substituting ,  and  in standard form of ellipse, we will get:

Therefore, the required equation of the ellipse in standard form would be .

b

step-by-step explanation: