Question

The points A-1,-9) and K(5,1) are endpoints of a diameter of circle 5. Which equation represents circle S?

A. (x - 2)2 + (y + 4)2 = 34
B. (x - 2)2 + (y + 4)2 = 136
C. (x + 2)2 + (-4)2 = 34
D. (x + 2)2 + (-4)2 = 136

Answer 1

A

Explanation:

if (x1,y1) and (x2,y2) are the extremities of diameter,then eq. of circle is

(x-x1)(x-x2)+(y-y1)(y-y2)=0

reqd. eq. is (x+1)(x-5)+(y+9)(y-1)=0

`x^(2) +x-5x-5+y^2+9y-y-9=0\\x^(2) -4x+y^2+8y-14=0\\compare with x^2+y^2+2gx+2fy+c=0\\center (-g,-f) \\radius r=√(g^2+f^2-c)`

center is (2,-4)

r=√(2²+(-4)²-(-14))

=√(4+16+14)

=√(34)

eq. of circle is (x-2)²+(y+4)²=34

or

(x²-4x)+(y²+8y)=14

(x²-4x+4)+(y²+8y+16)=14+4+16

(x-2)²+(y+4)²=34