Maths-
General
Easy
Question
The set of pointS on the axis of the parabola y2 = 4x + 8 from which the three normals to the parabola are all real and different is -
- {(k, 0) | k > –2}
- {(k, 0) | k > – 2}
- {(0, k) | k > –2}
- None of these
The correct answer is: None of these
The equation of the normal at (–2 + t2, 2t) is
y – 2t = 
·(x + 2 – t2) is
y – 2t = 
. (x + 2 – t2)
tx + y = 2t – 2t + t3
tx + y = t3
It passes through (k, 0), if tk = t3.
t(t2 – k) = 0.
It has three real values of t, if k > 0. So, the set of points (k, 0) is such that k > 0.
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