SOLUTION: Find an equation of the circle that has center (4,-6) and passes through (-3,-4)

Question 847330: Find an equation of the circle that has center (4,-6) and passes through (-3,-4)
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
The value for the radius is, using the Distance Formula, ;

Use knowledge of standard form for a circle. and the center is (h,k). Your example uses h=4 and k=-6. Watch the signs carefully.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
The standard form of the equation for a circle is:
where is the coordinate of the center of the circle , is the coordinate of the center of the circle, and is the radius of the circle .
the circle that has center (4,-6) and passes through (-3,-4)
given:
the center of the circle at ( ,)
one point the circle passes through: (,)
The only thing we are missing to complete the equation for the circle is to know (if given) or derive (if not given), , the radius of the circle.
With the two points given: center ( ,) and circle passes through (,) ; if we connect those two points together, that line will be equal the radius of the circle.
To determine the radius, think about a right triangle that has as its "" side and "" side the rise and run difference between the two given points. And, knowing the Pythagorean theorem to determine the hypotenuse of a right triangle:

We know that in in this instance the hypotenuse is equal to the radius of our circle, so we will substitute for .

If we take the square root of both sides of the previous equation we get:

To solve, you need:
= the difference in the two coordinates (from the two points given):

and = the difference in the two y coordinates (from the two points given):

then,

To return to the original problem: determine the equation for the circle with the given center point and passing through the given point:
which could be simplified to

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