Answer:
The equation of the circle is (x + 5) ² + (y + 7)² = 74 .
Option (C) is correct .
Step-by-step explanation:
The general equation of the circle is given by
(x - h) ² + (y - k)² = r²
Where (h,k) are the centre of the circle and r is the radius of the circle .
As given
A circle with center (-5, -7) that passes through the point (0, 0) .
As
\(r^{2}= (x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}\)
\(x_{1} = -5\)
\(y_{1} = -7\)
\(x_{2} = 0\)
\(y_{2} = 0\)
Put in the equation
\(r^{2}= (0-(-5))^{2} + (0-(-7))^{2}\)
\(r^{2}= (5)^{2} + (7)^{2}\)
\(r^{2}= 25+49\)
\(r^{2}=74\)
As center of the circle is (-5, -7) and r² is 74 .
Put in the general form of the equation .
(x -(-5)) ² + (y - (-7))² = 74
(x + 5) ² + (y + 7)² = 74
Therefore the equation of the circle is (x + 5) ² + (y + 7)² = 74 .
Option (C) is correct .
