Question

Write the equation of the circle with center (5,1) and a point on the circle at (8,-2). a) (x – 5)2 + (y – 1)2 = square root 18b) (x - 5)2 + (1 - 1)2 = 18 c) (x – 8)2 + (y + 2)2 = 18d) (x + 5)2 + ( + 1)2 = 18

Answer 1

The general equation of circle ,

$(x-x_1)^2+(y-y_1)^2=r^2$

The centre is

$(x_1,y_1_{}_{})$

The radius is r.

The distance between two points the centre and the point on the circle gives radius.

$r=\sqrt[]{(8-5)^2}+(-2-1)^2$$r=\sqrt[]{9+9}$$r^2=18$

The equation of cirlce formed is,

$(x-5)^2+(y-1)^2=18$

The correct option is b.