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A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?
A.
(-7, -1), 36 units
B.
(7, 1), 36 units
C.
(7, 1), 6 units
D.
(-7, -1), 6 units


Sagot :

nuhulawal20

The coordinates for the center of the circle and the length of the radius are  ( -7, -1 ) and 6 respectively.

Option D) is the correct answer.

What are the coordinates for the center of the circle and the length of the radius?

Given the equation;

x² + y² + 14x + 2y + 14 = 0

We subtract 14 from both sides

x² + y² + 14x + 2y + 14 - 14 = 0 -14

x² + y² + 14x + 2y = -14

Next, we complete the square for x² + 14

We have, ( x + 7 )² - 49

Next, we complete the square for y² + 2y

We have, ( y + 1)² - 1

We substitute these squares into the given equation

x² + y² + 14x + 2y = -14

( x + 7 )² - 49 + ( y + 1)² - 1 = -14

Collect like terms

( x + 7 )² + ( y + 1)² = -14 + 49 + 1

( x + 7 )² + ( y + 1)² = 36

( x + 7 )² + ( y + 1)² = 6²

Note that, the form of a circle is given as;

( x-h )² + ( y-k)² = r²

Hence, we match the values into the form and determine our center and radius.

( x-(+7) )² + ( y-(+1))² = 6²

( x-7 )² + ( y-1 )² = 6²

Hence Center = ( -7, -1 ) and radius = 6

The coordinates for the center of the circle and the length of the radius are  ( -7, -1 ) and 6 respectively.

Option D) is the correct answer.

Learn more about center and radius of circle here: https://brainly.com/question/10618691

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