Question

Find the equation for the circle with center (-4,-5) and passing through (4,-2)

Answer 1

Answer:

(x + 4)² + (y + 5)² = 73

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 4, - 5), thus

(x - (- 4))² + (y - (- 5))² = r², that is

(x + 4)² + (y + 5)² = r²

The radius is the distance from the centre to a point on the circle.

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (4, - 2)

r = $\sqrt{(4+4)^2+(-2+5)^2}$

  = $\sqrt{8^2+3^2}$

 = $\sqrt{64+9}$ = $\sqrt{73}$ ⇒ r² = 73, thus

(x + 4)² + (y + 5)² = 73 ← equation of circle

Answer 2

Answer: $(x+4)^{2} +(y+5)^{2} = 73$

Step-by-step explanation:

the formula for finding equation of circle is given as :

$(x-a)^{2}+(y-b)^{2} = r^{2}$

where ( a,b) is the coordinate of the center and r is the radius

The radius is the distance between the point and the center , the formula for calculating the distance between two points is given by :

d = $\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

d = $\sqrt{(4-(-4))^{2}+(-2-(-5))^{2}}$

$d = \sqrt{(4+4)^{2}+(-2+5)^{2}}$

$d = \sqrt{8^{2}+3^{2}}$

$d = \sqrt{73}$

since "r" is the distance , then

$r = \sqrt{73}$

The the equation of the circle , using the formula $(x-a)^{2}+(y-b)^{2} = r^{2}$ , will be

$(x+4)^{2} +(y+5)^{2} = 73$