Question

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

A. (x - 5)2 + (y - 7)2 = 74
B. (x + 5)2 + (y + 7)2 = 37
C. (x + 5)2 + (y + 7)2 = 74
D. (x - 5)2 + (y - 7)2 = 37

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

The equation of the circle is (x + 5) ² + (y + 7)² = 74 .

Option (C) is correct .

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 .