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Question

Parabola y2=4a(x−c1) and x2=4a(y−c2) where c1 and c2 are variables, touch each other. Locus of their point of contact is?

A
xy=a2
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B
xy=2a2
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C
xy=4a2
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D
xy=3a2
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Solution

The correct option is C xy=4a2
y2=4a(xc1)

and x2=4a(yc2) where C1 and C2 are variables, are such that they touch each other.

Locus of their point of contact is:

Equation of parabolas are : y2=4a(xC1)

and x2=4a(yC2)

where C1 and C2 are variables.

Here both the given curves touch each other at 2 points. At the point of contact (x,y), then the slope of both curves at (x,y) are the same.

y2=4a(xa)

differentiate wrt x

2yy=4a......(1)

X2=4A(y(2)) differentiate wrt x

2x=4ay.....(2)

solving (1) and (2),

xy=4a2

hence locus of the point of contact is xy=4a2

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