does anyone know the general form equation of a circle with a center (4,5) that passes through (-1,2)
...and just checking, would the standard form equation be:
(-1+4)^2 + (2+5)^2 = 58
No, the general equation would involve x and y variables. First get the radius of the circle from the distance between th center and the other point. That distance is
R = sqrt[4 -(-1)]^2 + (5-2)^2] = sqrt 34
The equation is
(x-x')^2 + (y-y')^2 = 34
where x' and y' are the coordinates of the center, 4 and 5.
(x-4)^2 + (y-5)^2 = 34
so the general form equation is
(x-4)^2 + (y-5)^2 = 34 ?
then what is the standard form?
General and standard form mean the same thing to me. The equation I wrote is for the specific circle that the problem asked for.
To find the general form equation of a circle with a center (h, k) and passes through a point (x1, y1), you can use the equation:
(x - h)^2 + (y - k)^2 = r^2
In this case, the center of the circle is (4, 5) and it passes through (-1, 2). To determine the radius (r), you can calculate the distance between the center and the point on the circle using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the distance between the center (4, 5) and the point (-1, 2) is:
Distance = √((-1 - 4)^2 + (2 - 5)^2)
= √((-5)^2 + (-3)^2)
= √(25 + 9)
= √34
Now you can substitute the values into the equation:
(x - 4)^2 + (y - 5)^2 = (√34)^2
Simplifying:
(x - 4)^2 + (y - 5)^2 = 34
Therefore, the general form equation of the circle with a center (4, 5) that passes through (-1, 2) is:
(x - 4)^2 + (y - 5)^2 = 34
Regarding your standard form equation, it seems to have an error. The standard form equation of a circle is:
(x - h)^2 + (y - k)^2 = r^2
Plugging in the values:
(-1 - 4)^2 + (2 - 5)^2 = 58
This simplifies to:
25 + 9 = 58
34 = 58
This equation is not correct, so the standard form equation you provided is not accurate.