Question

Write the equation of the circle with center (0, 0) and (5, 2) a point on the circle.

Answer 1

1. You have that:

r²=(x-h)²+(y-k)²

2. The center of this circle is (0,0), then:

h=0
k=0

3. When you substitute the values of h and k into the equation, you have:

r²=(x-h)²+(y-k)²
r²=(x-0)²+(y-0)²
r²=x²+y²

3. Now, you must find the radius "r".

4. You know that the point is (5,2), so:

r²=x²+y²

5. Finally:

√29=x²+y²

Answer 2

we know that
the equation of the circle with center (0, 0) is ---------> x²+y²=r²

Step 1
find the radius
the radius is simply the distance from the center to the point (5,2)
d=√[(5²+2²)]-------> d=√29
r=√29
the equation of the circle is
x²+y²=29

the answer is x²+y²=29