.
For what value of k the line 2x-y+k=0 is tangent to the parabola y^2=6x?
~~~~~~~~~~~~~~~~~~~~~
The key idea of solving this problem is that the system
2x - y + k = 0, (1)
= 6x (2)
must have one and only one solution.
(Then the solution will be the tangent point).
From equation (1), express 2x = y - k and substitute it into equation (2):
= 3*(2x), or
= 3*(y-k),
= 0.
The discriminant of this quadratic equation is
d = = 9 - 12k.
The condition of having the unique solution is d = 0, or
9 - 12k = 0,
which gives you k = = .
Answer. k = .
Parabola = 6x and the straight line 2x - y + = 0.
Ignore writing by "josgarithmetic" since his conception and explanation are WRONG.