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Monday, August 11, 2008

Q) A curve passes through (1, 1) such that triangle formed by the coordinate axes and tangent at any point of the curve is in the first quadrant and has its area equal to 2. Then the curve can be?

A)
Let the tangent equation be:
x/a + y/b = 1 ...........(where a and b are x and y intercepts respectively)

and ab/2 = 2 so ab = 4 ............(area of triangle)
bx + ay = ab
bx + ay = 4
one solution of this is x=1, y=1 as per question.
so
b + a = 4
Also, ab = 4
On solving, we get a = b = 2

So it can be a rectangular hyperbola, OR a straight line whose x intercept and y intercept both are 2 (ie. the line is x + y = 2).

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