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Chapter 1: Q 12. (page 50)

Write the standard form of the equation and the general form of the equation of each circle of radius rand center h,k.

Graph each circle.

r=3;(h,k)=(0,0)

Short Answer

Expert verified

Standard form of the circle is (x-0)2+(y-0)2=32

General form isx2+y2-9=0

Graph is as follows:

Step by step solution

01

Step 1. Given information

It is given thatr=3;(h,k)=(0,0)

02

Step 2. Standard from of the circle

The standard form the circle with center h,kand radius ris (x-h)2+(y-k)2=r2

It is given that r=3and h,k=0,0.

Therefore, the standard form of the circle is (x-0)2+(y-0)2=32

03

Step 3. General form of the circle

The general form of the circle is obtained by simplifying the standard form:

x2+y2=9

Subtract 9from both sides

x2+y2-9=0

04

Step 4. Graph of the circle

Graph is as follows:

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