How do you write the standard from of the equation of the circle given Center(4,7) and passing through (3,-2)?

1 Answer

Answer:

You need to find the radius first using the center and the point. then remember to use r squared for the radius portion.

Explanation:

#(x-4)^2 + (y-7)^2 = r^2#

Use the distance formula to find the radius (the pythagorean theorem). I like to draw the picture so it is easier to see the sides of the triangle and make the math easier.

graph{(x-4)^2 + (y-7)^2=sqrt(82) [-40, 40, -20, 20]}

The radius is #r=sqrt((3-4)^2+(-2-7)^2)#

#r=sqrt(1^2+9^2)=sqrt(82)#

So the equation is: #(x-4)^2+(y-7)^2=82#