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Question

Minimum distance between the curves y2=4x and x2+y212x+31=0 is

A
5
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B
21
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C
285
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D
215
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Solution

The correct option is A 5
Centre and radius of the given circle is P(6,0) and 5, respectively.

Now the minimum distance between two curves always occurs along a line that normal to both the curves.

Equation of normal to y2=4x at (t2,2t) is

y=tx+2t+t3.

If it is normal to circle also, then it must pass through (6,0).

0=t34tt=0 or t=±2.

A(4,4) and C(4,4)

PA=PC=20=25

Required minimum distance =255=5.

729601_670287_ans_cb56cdc060984ac788f0dff8dc1acb52.png

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