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Chapter 10: Q. 6 (page 698)

Identify each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci; if it is a hyperbola, give its center, vertices, foci, and asymptotes.

x2-4x=2y

Short Answer

Expert verified

The vertex is 2,-2, focus is2,-32and directrix isy=-52.

Step by step solution

01

Step 1. Given Information

We are given the equation x2-4x=2y.

We need to find the type of conic.

02

Step 2. Determining the conic

Rewriting the equation we get:

x2-4x=2y鈬�x2-4x+4=2y+4鈬�x-22=2(y+2)

This is the equation of a parabola. Comparing it with the standard equationx-h2=4a(y-k) we get:

h=2,4a=2鈬�a=24=12k=-2

03

Step 3. Finding vertex, focus, and directrix 

Vertex is h,k=(2,-2).

Focus is h,k+a=2,-2+12=2,-32.

Directrix is

y=k-a鈬�y=-2-12鈬�y=-52

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Most popular questions from this chapter

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

10x2-12xy+4y2-x-y-10=0

In Problems 43鈥�52, identify the graph of each equation without applying a rotation of axes.

3x2-2xy+y2+4x+2y-1=0

Graph each function.

f(x)=9-9x2.

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

y2=8x

In Problems 15鈥�18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

Ax24-y2=1Bx2-y24=1Cy24-x2=1Dy2-x24=1

Graph:
See all solutions

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