-a circle with center at the point O(0,0) also has the point P(-2,3) on it. The equation of this circle is?
and a second question:
-A circle has a center of square root 5. The equation of this circle is?
Please help me.
the general equation of a circle with centre at (0,0) is
x^2 + y^2 = r^2
sub in your given point to find r^2 and you are done.
your second question makes no sense
the centre of a circle is a position, not a value.
To find the equation of a circle, we need to use the general formula:
(x - h)^2 + (y - k)^2 = r^2,
where (h, k) represents the center of the circle and r is the radius.
For the first question:
We are given the center of the circle at O(0,0) and a point on the circle P(-2,3).
1. Find the center:
Since we are given the center at O(0,0), we know that (h, k) = (0, 0).
2. Find the radius:
To find the radius, we can use the distance formula. The distance between O(0,0) and P(-2,3) is given by:
r = sqrt((x2-x1)^2 + (y2-y1)^2).
Substituting the coordinates: r = sqrt((-2-0)^2 + (3-0)^2) = sqrt(4+9) = sqrt(13).
3. Substitute the values in the equation:
(x - h)^2 + (y - k)^2 = r^2.
(x - 0)^2 + (y - 0)^2 = (sqrt(13))^2.
x^2 + y^2 = 13.
Therefore, the equation of the circle is x^2 + y^2 = 13.
For the second question:
We are given the center of the circle as sqrt(5).
1. Find the center:
Since we are given the center at sqrt(5), we know that (h, k) = (sqrt(5), sqrt(5)).
2. The radius:
We are not given the radius in this case, so we cannot determine the equation of the circle without additional information.
To calculate the equation of the circle, we would need to know the radius or have another point on the circle. Without this information, we cannot provide the equation of this circle.