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The shortest distance between the parabolas y^2=4x and y^2=2x-6 is

The shortest distance between the parabolas y^2=4x and y^2=2x-6 is 

Grade:11

1 Answers

Latika Leekha
askIITians Faculty 165 Points
8 years ago
Hello student,
The given parabolas are y2 = 4x and y2 = 2x – 6 is
Normal to y2 = 4x at (m2, 2m) is y + mx – 2m – m3 = 0
Normal to y2 = 2x – 6 = 2(x-3) at (m2/2 + 3, m) is y + (x-3) – m – m3/2 = 0
i.e. y + mx – 4m – m3/2 = 0
Now, for both to be coomon or same , we have
– 2m – m3 = – 4m – m3/2
This gives, m(m-2)(m+2) = 0
This gives m = 0, 2, -2.
So, points will be (4, 4) (5, 2).
Hence, the shoretst distance = √12 + 22 = √5 units.

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