A circle C is defined by the equation x^2+y^2-8x-4y+10=0
a) Find the coordinates of its center and its radius.
b) Show that the gradient m of the tangents of this circle which pass from the origin obey the equation 10(m^2+1)=(4m-2)^2
c) Hence show that these two tangents are perpendicular.
So far I managed:
x^2+y^2-8x-4y+10=0
(x^2-8x+16) + (y^2 -4y + 4) + 10 -16-4=0
(x-4)^2+ (y-2)^2= 10
The centre of the circle is at x=4, y=2
THANKS
a) Find the coordinates of its center and its radius.
b) Show that the gradient m of the tangents of this circle which pass from the origin obey the equation 10(m^2+1)=(4m-2)^2
c) Hence show that these two tangents are perpendicular.
So far I managed:
x^2+y^2-8x-4y+10=0
(x^2-8x+16) + (y^2 -4y + 4) + 10 -16-4=0
(x-4)^2+ (y-2)^2= 10
The centre of the circle is at x=4, y=2
THANKS