General Form of a circle

Question

What is the equation, in general form, of the circle whose center is the origin and which contains the point (-3,4)?

Answer 1

The general formula for a circle is (x-a)² + (y - b)² = radius²

 

however the center is the origin, which is (0,0) and the formula becomes

 

(x)² + (y )² = radius2, To find the radius squared, we simply substitute the values for x and y that lie on the circle

 

3² + 4² =  25

 

Therefore the equation becomes:

 

x² + y² = 25

Answer 2

(x-h)^2+(y-k)^2=r^2

(h,k) is the center and the circle contains point (-3,4)

find the radius using the distance formula

√[(-3-0)^2+(4-0)^2]

√(9+16)=√25=5

r=5

(x-0)^2+(y-0)^2=5^2

x^2+y^2=25