   Chapter 10.5, Problem 41E

Chapter
Section
Textbook Problem

# Find an equation for the conic that satisfies the given conditions.41. Ellipse, center (−1, 4), vertex (−1,0), focus (−1, 6)

To determine

To Find: The equation for the conic using the center (1,4) , focus (1,6) and the vertex (1,0) of the ellipse.

Explanation

Given:

The center (1,4) , focus (1,6) and the vertex (1,0) of the ellipse.

Calculation:

Since, the x coordinate of the focus and vertex is same and equal to 1 . Then the value of h is 1 and the foci and vertices are located in y axis.

Compute the value of c foci equation.

foci=(h,(k±c))

Substitute the value (1,4) for (h,k) and (1,6) for focus.

(1,6)=(h,(k+c))h=1(4+c)=6c=64c=±2

Therefore the value of c is ±2 .

Compute the value of a using the vertices equation:

vertices=(h,(k±a))

Substitute the value of (1,4) for (h,k) and (1,0) for vertex.

(1,0)=(1,(4±a))(4±a)=0a=±4

Therefore, the value of a is ±4

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