Question

HELP! Identify the equation of the circle that has its center at (-3, -4) and passes through the origin.
A. (x−3)^2+(y−4)^2=25
B. (x+3) ^2+(y+4)^2=25
C. (x−3) ^2+(y−4)^2=5
D. (x+3) ^2+(y+4)^2=5

Answer 1

Answer:

Option B. (x+3) ^2+(y+4)^2=25

Step-by-step explanation:

we know that

The equation of the circle in standard form is equal to

$(x-h)^{2}+(y-k)^{2}=r^{2}$

where

(h,k) is the center and r is the radius

step 1

Find the radius of the circle

Remember that the distance of the center and any point on the circle is equal to the radius of the circle

so

Find the distance between the points (-3,-4) and (0,0)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute

$r=\sqrt{(0+4)^{2}+(0+3)^{2}}$

$r=\sqrt{(4)^{2}+(3)^{2}}$

$r=\sqrt{25}$

$r=5\ units$

step 2

Find the equation of the circle

$(x-h)^{2}+(y-k)^{2}=r^{2}$

the center is the point (-3,-4) and the radius is r=5 units

substitute

$(x+3)^{2}+(y+4)^{2}=5^{2}$

$(x+3)^{2}+(y+4)^{2}=25$