   Chapter 10, Problem 47RE

Chapter
Section
Textbook Problem

Find the foci and vertices and sketch the graph.47. 6y2 + x − 36y + 55 = 0

To determine

To find: The focus and vertex and sketch the graph of equation 6y2+x36y+55=0 .

Explanation

Given:

The given equation is as follows.

6y2+x36y+55=0 (1)

Calculation:

Rewrite equation (1) to a standard form.

6y2+x36y+55=06y236y+55=x6y236y+551=x1

6y236y+54=(x+1)6(y26y+9)=(x+1)6(y3)2=(x+1)

(y3)2=16(x+1)(y3)2=44×16(x+1)

(y3)2=4(124)x+1 (2)

This is the equation of a parabola.

The standard equation of the parabola is as follows,

(yh)2=4p(xk) (3)

Here, h,k is the vertex of the parabola.

Compare the equation (2) and (3).

Vertex points is at (h,k)=(1,3) .

p=124

Determine the focus.

The focus is at (h+p,k)=((1124),3)=(2524,3)

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