What are the points of intersection of the circle x^2 - 6x + y^2 - 8y = 24 with the axes.
The equation of the circle is x^2 - 6x + y^2 - 8y = 24.
Where the circle intersects the x-axis the y-coordinate is 0.
x^2 - 6x = 24
=> x^2 - 6x - 24 = 0
x1 = (6 + sqrt(36 + 96))/2
=> 3 + sqrt 33
x2 = 3 - sqrt 33
Where the circle intersects the y axis the x-coordinate is 0
y^2 - 8y = 24
=> y^2 - 8y - 24 = 0
y1 = 4 + sqrt 160/2 = 4 + sqrt 40
y2 = 4 - sqrt 40
The x-intercepts of the circle are (3 + sqrt 33, 3 - sqrt 33) and the y-intercepts of the circle are (4+sqrt 40, 4 - sqrt 40)
we substitute y=0 when circlre intersects the x_axis :
=>the x-interceptsof the circlr are (3+sqrt33,3-sqrt33)
and we need substitute x=0
when circle intersects the y_axis
=>the y_intercecepts of the circle are (4+2 sqrt10,4-2 sqrt10)