Write the standard form of the equation of the circle with the center (0,2) that passes through (7,3)

x²+y²-4y-46=0

Step-by-step explanation:

the equation of a circle is in the form (x - a)² + (y - b)² = r², where (a,b) is the center of the circle

the equation is (x - 0)² + (y - 2)² = r², where r is the radius. But r is the distance from (0,2) to (7,3)

the distance from two points is given by r² = (x₁ -x₂)² + (y₁ - y₂)²

r²= (0 - 7)² + (2 - 3)²

r² = 49 + 1 = 50

hence the equation is  

                  (x)² + (y - 2)² = 50

                  x²+y²-4y+4 = 50

                 x²+y²-4y-46= 0