Question

The equation of common tangent to the curve xy = 4 and x2 + y2 = 8, whose x and y intercepts are positive is x + y = λ. Find the value of λ.

Answer 1

Any point on the curve xy = 4 is (2t, 2/t)

slope of the tangent at (2t, 2/t) is - 1/t2

∴ equation of tangent is x + t2y - 4t = 0 since it is tangent to x2 + y2 = 8 also

i.e. t2 = 1

∴ equation of the tangent is x + y = ± 4 Since the intercepts are positive

∴ the tangent is x + y = 4