The center of a circle and a point on the circle are given. Write the equation of the circle in standard form. center: (2,-2), point on the circle: (5,3)

 To write the equation of the circle in standard form, we need the coordinates of the center (h, k) and the radius r. The standard form of the equation of a circle is given by:

(x - h)² + (y - k)² = r²

You've already given the coordinates of the center, which are (h, k) = (2, -2).

Now, we need to find the radius of the circle. The radius can be found by calculating the distance between the center of the circle and the point on the circle. The distance formula is:

distance = √[(x2 - x1)² + (y2 - y1)²]

Let's calculate the radius using the given points, center (2, -2) and point on the circle (5, 3):

radius = √[(5 - 2)² + (3 - (-2))²] radius = √[(3)² + (5)²] radius = √[9 + 25] radius = √34

Now we have the radius and the center, so we can write the equation of the circle in standard form:

(x - 2)² + (y + 2)² = (√34)² (x - 2)² + (y + 2)² = 34

This is the equation of the circle in standard form.