Question

Which is an equation of a circle with center (-5, -7) that passes through the point (0, 0)?

Answer 1

Hello,

Let's calculate the radius:

r²=5²+7²=74

The circle's equation is (x+5)²+(y+7)²=74

Answer C

Answer 2

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 .