Math Problem 4?

Question

Write equation for:

The circle having center (-3, 4) and passing through the origin

Answer 1

(x + 3)^2 + (y - 4)^2 = 25

The general equation of a circle centered at (h, k) is:

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

They gave you the center (-3, 4) so all that's left is to figure out r^2.

(x + 3)^2 + (y - 4)^2 = r^2

Since the circle passes through the origin, the point (0,0) has to fit the equation, so:

(0 + 3)^2 + (0 - 4)^ = r^2
9 + 16 = r^2
25 = r^2

Answer 2

1) Figure out the radius, it's the distance between the center and any point on the circle. You've been told about one of these points...
2) Plug into the equation for a circle centered at (x0,y0) and radius r.

Answer 3

With it passing through orgin (0,0), then you know the radius is squareroot((-3-0)^2+(4-0)^2) = sqr(9+16)=sqr25 = 5.

So, the equation is (x+3)^2+(y-4)^2=5^2=25...