   Chapter 10.5, Problem 34E

Chapter
Section
Textbook Problem

# Find an equation for the conic that satisfies the given conditions.34. Parabola, focus (2, −1), vertex (2, 3)

To determine

To Find: The equation for the conic using the vertex (2,3) and focus (2,1) of the parabola.

Explanation

Given:

The Vertex is (2,3) and focus is (2,1) of the parabola.

Calculation:

The value of x coordinate of vertex and focus are same, so the h value is 2 .

Compute the distance from the focus to the vertex.

p=focusofyaxisvertexofyaxis

Substitute 1 for focus of y axis and 3 for vertex of y axis in above equation.

p=13p=4

Compute the value of k using the below focus equation.

Focus=(h,k+p)(2,1)=(h,k+p)

The value of h=2 .

(k+p)=1 (1).

Substitute the value 4 for p in equation (1).

(k+(4))=1k=1+4k=3

The focus of the parabola is like (0,p)

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