Q18 of 149 Page 16

The curves y = ae^x and y = be^–x cut orthogonally, if

Given that the curves y = ae^x and y = be^–x

Differentiating both of them w.r.t. x,

Let m₁=ae^x and m₂=-be^-x

m₁×m₂=-1

(Because curves cut each other orthogonally)

⇒ -ab = -1

⇒ ab = 1

If the line y = x touches the curve y = x² + bx + c at a point (1, 1) then

The slope of the tangent to the curve x = 3t² + 1, y = t³ – 1 at x = 1 is

The equation of the normal to the curve x = acos³ θ, y = a sin³θ at the point is

If the curves y = 2 e^x and y = ae^–x interest orthogonally, then a =

The curves y = aex and y = be–x cut orthogonally, if