write the equation in standard form for the circle with center (0,7) passing through (0, 3/2)
To write the equation of a circle in standard form, you need two key pieces of information: the center coordinates and the radius. The general equation for a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
In this case, you are given the center coordinates (0,7) and a point on the circle (0,3/2). To find the radius, you can use the distance formula between the center and the given point:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates:
r = sqrt((0 - 0)^2 + (3/2 - 7)^2)
= sqrt((0 - 0)^2 + (-11/2)^2)
= sqrt(0 + 121/4)
= sqrt(121/4)
= 11/2
Therefore, the radius of the circle is 11/2.
Now, substitute the center coordinates (h, k) = (0, 7) and the radius r = 11/2 into the equation of a circle to get:
(x - 0)^2 + (y - 7)^2 = (11/2)^2
x^2 + (y - 7)^2 = 121/4
Thus, the equation in standard form for the circle with center (0,7) passing through (0, 3/2) is x^2 + (y - 7)^2 = 121/4.