Find the standard form of the equation of the circle with the given characteristics.
Center: (5, -2); point on circle: (-3, -4)
You know the equation must have the form
(x-5)^2 + (y+2)^2= r^2
plug in the given point to find r^2 and you are done.
Hey i got 68 as the radius. So im guessing 68 is the answer right?
To find the standard form of the equation of a circle, we need to know the center and either the radius or a point on the circle. In this case, we are given the center (5, -2) and a point on the circle (-3, -4).
To find the radius, we can use the distance formula, which is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of two points. In this case, let's use the center as (x1, y1) and the point on the circle as (x2, y2).
Substituting the values, we have:
d = √(((-3) - 5)^2 + ((-4) - (-2))^2)
= √((-8)^2 + (-2)^2)
= √(64 + 4)
= √68
= 2√17
The radius of the circle is 2√17.
Now, we can use the standard form equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) are the coordinates of the center, and r is the radius.
Substituting the values we have:
(x - 5)^2 + (y - (-2))^2 = (2√17)^2
(x - 5)^2 + (y + 2)^2 = 68
Therefore, the standard form of the equation of the circle is (x - 5)^2 + (y + 2)^2 = 68.