Question

the equation of a circle is
${x}^{2} + y2 + 14x + 2y + 14 = 0$
what are the coordinates for the center of the circle and the length of the radius
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Answer 1

Answer:

The answer is

center = ( - 7 , - 1)

radius = 6

Step-by-step explanation:

The general equation of a circle is given by

x² + y² + 2gx + 2fy + c = 0

where the center of the center of the circle is given by

( - g , - f)

From the question the equation is

x² + y² + 14x + 2y + 14 = 0

Comparing with the general equation above we have

2g = 14 2f = 2

g = 7 f = 1 c = 14

So the center of the circle is

( - 7 , - 1)

The radius of a circle is given by

$r = \sqrt{ {g}^{2} + {f}^{2} - c}$

where

g = 7

f = 1

c = 14

Substitute the values into the above formula

That's

$r = \sqrt{ {7}^{2} + {1}^{2} - 14 } \\ r = \sqrt{49 + 1 - 14} \\ r = \sqrt{36}$

we have the final answer as

radius = 6

Hope this helps you