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.Com
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) (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)
RELATED QUESTIONS
What is the general form of the equation of a circle with its center at (-2, 1) and... (answered by josgarithmetic)
Show that the line y=4x+17 is a tangent to the parabola with equation... (answered by ikleyn)
Show that the line y = 10 − 3x is tangent to the circle x2 + y2 = 10. Find an equation... (answered by greenestamps)
How do i do question number 77 on 10.3
Write an equation of the line that is tangent to... (answered by jim_thompson5910,Alan3354)
Find the equation of the line tangent to a circle x2 + y2 = 13 at... (answered by josgarithmetic)
Write the equation of the line that is tangent to the circle x2 + y2 = 100 at the point... (answered by josgarithmetic)
Find the equation of the tangent line to the circle whose equation is x2 + y2 - 18x +... (answered by lwsshak3)
Which of these is the equation for a line tangent to the circle x2 + y2 = 20 at point (2, (answered by josgarithmetic)
The line mx-y=0 is tangent to the circle X2+Y2-6X+2y+2=0 find the two values of... (answered by KMST)