Question

Find the x intercept of a circle.(x−5)^2+(y+6)^2=40

 

Answer 1

Circle equation is

(x - 5)^2 + (y + 6)^2  =  40

To get the x - intercept of a circle put y = 0 in above equation

(x - 5)^2 + (0 + 6)^2  =  40

x^2 - 10x + 25 + 36  =  40

x^2 - 10x + 25 + 36 - 40  =  0

x^2 - 10x + 21  =  0

x^2 - 7x - 3x + 21  =  0

x(x - 7) - 3(x - 7)  =  0

(x - 7)(x - 3)  =  0

(x - 7)  =  0      ;      (x - 3)  =  0

x  =  7               ;       x  =  3

Answer :

The x - intercepts of a circle are x  =  7  and   x  =  3.