Question

Find the length of the radius of a circle whose center is at (3,4) and passes through (-3, -4)

Answer 1

The length of the radius is given by the Pythagoras formula which take the radius as the hypotenuse.

radius = $\sqrt{[x_{1}- x_{2}]^2+[ y_{1} - y_{2}]^2 }$
radius = $\sqrt{(3--3)^2+(4--4)^2}$
radius = $\sqrt{6^2+8^2}$
radius = $\sqrt{36+64}$
radius = $\sqrt{100}$
radius = 10

Answer 2

The equation of a circle is: (x - xo)^2 + (y - yo)^2 = r^2

Where xo and yo are the coordinates of the center = (3,4).

r is the radius of the circle and you can find it using the equation of the distance between the point (-3,-4) and the center (3,4):

r^2 = (-3 -3)^2 + (-4 - 4)^2 = 6^2 + 8^2 = 36 + 64 = 100.

=> r = √100

=> r = 10

Answer: r = 10