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Question

The number of mutually perpendicular tangents that can be drawn from the curve y=||1ex|2| to the parabola x2=4y is

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Solution

Mutually perpendicular tangents can be drawn from a part on the directrix. So, we should find the number of intersection points of y=||1ex|2| and y=1.
Now, y=|1ex|2 or y=2|1ex|
For y=1
1ex=±3 or 1ex=±1
​​​​​​​On solving
1ex=3 (not possible) (ex>0)
1ex=3 (possible)
1ex=1 (not possible) (ex>0)
1ex=1 (possible)
Number of intersections =2.

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