x2+y2−2x−6y−6=0 x and y intercepts??

x² + y² - 2x - 6y - 6 = 0

When y = 0 :
x² - 2x - 6 = 0
x = [2 ± √(2² + 4*1*6)]/2
x = 1 ± √7
x-intercepts = 1 + √7 and 1 - √7

When x = 0 :
y² - 6y - 6 = 0
y = [6 ± √(6² + 4*1*6)]/2
y = 3 ± √15
y-intercepts = 3 + √15 and 3 - √15

Use the caret ^ (above the 6) to denote an exponent !

equation of a CIRCLE: x^2 + y^2 - 2x - 6y - 6 = 0

(x - 1)² + (y - 3)² = 16

when x = 0, y = 3 ± √15

when y = 0, x = 1 ± √7

　
To find x-intercepts, set y = 0
x² − 2x − 6 = 0
x² − 2x = 6
x² − 2x + 1 = 7
(x − 1)² = 7
x − 1 = ± √7
x = 1 ± √7

To find y-intercepts, set x = 0
y² − 6y − 6 = 0
y² − 6y = 6
y² − 6y + 9 = 15
(y − 3)² = 15
y − 3 = ± √15
y = 3 ± √15

y-intercept: set x=0
y^2-6y-6 = 0

This equation is of form ay^2+by+c=0
a = 1 b = -6 c = -6
y=[-b+/-sqrt(b^2-4ac)]/2a]
y=[6 +/-sqrt(-6^2-4(1)(-6)]/(2)(1)
discriminant is b^2-4ac =60
y=[6 +√(60)] / (2)(1)
y = 3 + √15
y=[6 -√(60)] / (2)(1)
y = 3 - √15

y-intercepts are:
(0, 3+√15) and (0, 3- √15)

x-intercept:
set y=0
x^2-2x - 6 = 0

This equation is of form ax^2+bx+c=0
a = 1 b = -2 c = -6
x=[-b+/-sqrt(b^2-4ac)]/2a]
x=[2 +/-sqrt(-2^2-4(1)(-6)]/(2)(1)
discriminant is b^2-4ac =28
x=[2 +√(28)] / (2)(1)
x = 1 + √7
x=[2 -√(28)] / (2)(1)
x = 1 - √7

x-intercepts are:
( 1 + √7 , 0) and ( 1 - √7 , 0)