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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Finding the Standard Equation of an Ellipse In Exercises 17-20, find the standard form or the equation of the ellipse with the given characteristics.

Center: (0, 1)

Focus: (4, 1)

Vertex: (6, 1)

To determine

To calculate: The equation of ellipse whose center is at (0,0), focus is at (5,0) and vertex is at (7,0).

Explanation

Given:

The coordinates of center are (0,0), focus are (5,0) and vertex are (7,0) for the ellipse.

Formula used:

Equation of ellipse is (xh)2a2+(yk)2b2=1, where any arbitrary point is (x,y), (h,k) is the center, 2a and 2b are lengths of major and minor axes respectively.

The property, (ab)2=a22ab+b2.

Calculation:

Consider coordinates of center that is (0,0), focus are (5,0) and vertex are (7,0) for the ellipse.

In standard equation of ellipse (h,k) is center, its provided that (0,0) is the center for which equation is to be evaluated so compare to get,

h=0 and k=0.

Coordinates of vertex are given by (h+a,k) its provided that (7,0) is the vertex of ellipse so compare to get

(h+a,k)=(7,0).

Substitute 0 for h and 0 for k.

(0+a,0)=(7,0)(a,0)=(7,0)a=7

As foci lie on major axis, so

(h+c,k)=(5,0)

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