what is the center of a circle with the following equation?

Question

_{(x-1)²+(y+2)²=49}

 

Answer 1

Hi Zach,

 

The equation for a circle centered at the origin on a coordinate plane is

 

x^2 + y^2 = radius^2

 

so, we can tell from your original equation that the radius of the circle is 7, because 7^2 = 49.

 

Just like moving a parabola using the y=x^2 equation, if we change the circle equation to

 

(x-1)^2 + (y+2)^2 = 49

 

we move it 1 unit to the right, and two units down. So since the center started at (0,0) the new center will be (1,-2). Hope this helps!

 

Kate

Answer 2

I would say that the equation of a circle with center at (h,k) is (x-h)^2 + (y-k)^2 = r^2. In our  case h=1 and k equal to -2, the center will be at (1,-2)

CHECK!!!!!!!!!!!!!!!!!

Answer 3

The standard form for a circle of radius seven centered around the origin is xsquared plus y squared equals the radius squared (49). Why does this work? Let's test a few points Off the x,y axis: (7,0) (-7,0) ((0,7) (0,-7)

 

These are the four points of the circle intersecting the two lines dividing the circle in half. So we need values of x and y that create that same (0, +/-7) (+/-7,0)

 

In this case we find x=1 and y=-2 the intersection for the two lines is the center.

 

Hope that helps,

Deanna