SOLUTION: The homework question is,Show that the line with equation y=2x-10 is a tangent to the circle with equation x2+y2-4x+2y=0 and establish the coordinates of the point of contact. x2 m

Algebra ->  Circles -> SOLUTION: The homework question is,Show that the line with equation y=2x-10 is a tangent to the circle with equation x2+y2-4x+2y=0 and establish the coordinates of the point of contact. x2 m      Log On


   

Question 387399: The homework question is,Show that the line with equation y=2x-10 is a tangent to the circle with equation x2+y2-4x+2y=0 and establish the coordinates of the point of contact. x2 means x squared and y2 means y squared. Can you provide a solution with working please?
Many Thanks,
Andrew.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
substituting ___ x^2 + (2x - 10)^2 - 4x + 2(2x - 10) = 0

x^2 + 4x^2 - 40x + 100 - 4x + 4x - 20 = 0

5x^2 - 40x + 80 = 0

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

y = 2(4) - 10 = -2

since there is only one solution for x , there is only one point of contact between the line and the circle
this defines the tangent

the point of tangency is (4,-2)