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Circle x2 + y2 + 2kx = O, k€R touches the parabola y2 = 4x externally, then (1)k>0 (2)k1

Circle x2 + y2 + 2kx = O, k€R touches the parabola y2 = 4x externally, then (1)k>0 (2)k1

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
Put  y2 = 4x into the circle eqn.,
that is:
x^2 + 4x + 2kx = 0
The discriminan should be zero if it touches thee circle.
Therefore,
4(k+2)^2 – 4*1*0 = 0
(k+2)^2 = 0
k = -2
whic is negative hence k would be negative.

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