# The equation for the given circle with center ( 2 , − 5 ) and radius 2

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 104RE
To determine

## To calculate:The equation for the given circle with center (2,−5) and radius 2

Expert Solution

The equation for the given circle with center (2,5) and radius 2 is x2+y24x+10y+27=0

### Explanation of Solution

Given information:

A circle with center (h,k)=(2,5) and radius r=2

Formula used:

For a given circle with center (h,k) and radius r the equation is given as:

(xh)2+(yk)2=r2

This is referred to as the Standard form for the equation of a given circle.

Moreover, if the center of the circle is nothing but the origin that is (0,0) then the equation reduces to:

x2+y2=r2

Calculation:

Consider the given circle with center (h,k)=(2,5) and radius r=2

Recall that for a given circle with center (h,k) and radius r the equation is given as:

(xh)2+(yk)2=r2

Therefore, replacing the values we get:

(x2)2+(y(5))2=(2)2(1)

Now using the following formulae:

(a+b)2=a2+2ab+b2(ab)2=a22ab+b2

Then, (1) reduces to:

x2+44x+y2+25+10y=2x2+y24x+10y+29=2x2+y24x+10y+292=0x2+y24x+10y+27=0

Hence, the equation for the given circle with center (2,5) and radius 2 is:

x2+y24x+10y+27=0

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