How do you write an equation with center is (4,-1) and solution point is (1,4)?

1 Answer
Dec 25, 2016

I am going to assume that you want the equation of a circle. Please see the explanation.

Explanation:

The standard Cartesian form for the equation of a circle is:

(xh)2+(yk)2=r2 [1]

where x and y are any point, (x,y), on the circle, h and k are the center point, (h,k), and r is the radius.

Substitute 4 for h and -1 for k into equation [1]:

(x4)2+(y1)2=r2 [2]

To find the value of r, substitute 1 for x and 4 for y into equation [2], then solve for r:

(14)2+(41)2=r2

32+52=r2

r2=36

r=6

Substitute 6 for r into equation [2]:

(x4)2+(y1)2=62 [3]

Equation [3] represents the desired circle.