Write the standard form of the equation of the circle that passes through (0,4) and has its center at (-3, -1)
(x+3)^2+(y+1)^2=sqrt34
correct.
yes it is
5x5=25
To find the equation of a circle given its center and a point on the circle, you can use the formula:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) are the coordinates of the center of the circle, and r is the radius of the circle.
In this case, the center of the circle is (-3, -1) and the point (0, 4) lies on the circle. Let's calculate the radius:
r = √[(x - h)^2 + (y - k)^2]
= √[(0 - (-3))^2 + (4 - (-1))^2]
= √[(3)^2 + (5)^2]
= √[9 + 25]
= √34
Now we can substitute the values into the standard form equation:
(x - (-3))^2 + (y - (-1))^2 = (√34)^2
(x + 3)^2 + (y + 1)^2 = 34
Therefore, the standard form of the equation of the circle is (x + 3)^2 + (y + 1)^2 = 34.