Question

What is the center and radius of the circle? (x-4)^2 + (y-7)^2 =49

Answer 1

The center of circle is: (-7,4) and Radius is 7 units

or (-4,7) and Radius is 7 units

We have to compare the given equation of circle with standard equation of circle

Given equation is:

2nd pic

down below

Standard equation of circle is:

3rd pic

down below

Here

h and k are coordinates of center of circle

So,

comparing

1st pic

down below

Hence,

The center of circle is: (-7,4) and Radius is 7 units

Keywords: Circle, radius

Answer 2

The center is ( 4 , 7)

The radius is 7

Explanation:

First expand the equation

That's

( x - 4)² + ( y - 7)² = 49

x² - 8x + 16 + y² - 14y + 49 - 49 = 0

x² + y² - 8x - 14y + 16 = 0

Comparing with the general equation of a circle

x² + y² + 2gx + 2fy + c = 0

2g = - 8 2f = - 14

g = - 4 f = - 7 c = 16

Center of a circle is ( - g , - f)

( --4 , --7)

Which is ( 4 , 7)

The radius of the circle is given by

r = √g² + f² - c

Where r is the radius

r = √ (-4)² + (-7)² - 16

= √16 + 49 - 16

= √49

= 7

Hope this helps you