SOLUTION: Write the equation of a circle that passes through (7,-1) and has its center at (-2,4).
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Question 636105: Write the equation of a circle that passes through (7,-1) and has its center at (-2,4).
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the general equation of a circle.
Plug in and (since the center is the point (h,k) ).
Plug in and (this is the point that lies on the circle, which is in the form (x,y) ).
Combine like terms.
Square each term.
Add.
So because , , and , this means that the equation of the circle with center (-2,4) that goes through the point (7,-1) is
.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The distance from the center of a circle to a point on the circle is the radius. So use the distance formula
^2\ +\ (y_1\ -\ y_2)^2})
where )
and )
are the coordinates of the given points to determine the radius, then use the standard form of an equation of a circle centered at )
with radius 
to write your desired equation:
^2\ +\ \left(y\ -\ k\right)^2\ =\ r^2)
John
My calculator said it, I believe it, that settles it
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