find an equation of a circle satisfying the given conditions. Center(0,0), containing (-3,4)
Hint: the radius of the circle is 5.
x^2 + y^2 = ?
To find an equation of a circle that satisfies the given conditions, we can use the formula for a circle centered at (h, k) with radius r:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center is (0, 0), so we have h = 0 and k = 0. The circle also contains the point (-3, 4), which means it is on the circle. We can substitute this point into the equation to find the radius.
Substituting (-3, 4) into the equation, we have:
(-3 - 0)^2 + (4 - 0)^2 = r^2
9 + 16 = r^2
25 = r^2
So the radius squared is 25, which means the radius itself is 5.
Therefore, the equation of the circle is:
(x - 0)^2 + (y - 0)^2 = 5^2
x^2 + y^2 = 25