Find the equation for the circle with center (1,2) and passing through (-4,-3).
Write the equation for the circle.
(x-1)^2+(y-2)^2 = r^2
(-4-1)^2 + (-3-2)^2 = r^2
that should get you under way.
radius=sqrt(5^2 + 5^2)=5sqrt2
(y-2)^2 + (x-1)^2=(5sqrt2)^2
To find the equation for the circle with center (1,2) and passing through (-4,-3), we can use the general equation of a circle which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the center of the circle, and r represents the radius.
Given that the center of the circle is (1,2), we can substitute these values into the equation:
(x - 1)^2 + (y - 2)^2 = r^2
Now, we need to find the radius of the circle. The radius is the distance between the center of the circle and any point on the circumference of the circle. In this case, we are given that the circle passes through the point (-4,-3). We can use the distance formula to find the distance between the center (1,2) and the point (-4,-3):
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates:
d = sqrt((-4 - 1)^2 + (-3 - 2)^2)
= sqrt((-5)^2 + (-5)^2)
= sqrt(25 + 25)
= sqrt(50)
The radius is the square root of 50.
Substituting everything back into the equation of the circle, we have:
(x - 1)^2 + (y - 2)^2 = (√50)^2
(x - 1)^2 + (y - 2)^2 = 50
Therefore, the equation for the circle with center (1,2) and passing through (-4,-3) is (x - 1)^2 + (y - 2)^2 = 50.