The point on the curve y = 6x – x2 at which the tangent to the curve is inclined at to the line x + y = 0 is

Q21 of 149 Page 16

The point on the curve y = 6x – x² at which the tangent to the curve is inclined at to the line x + y = 0 is

The curve y = 6x – x² has a point at which the tangent to the curve is inclined at to the line x + y = 0.

Differentiating w.r.t. x,

On solving we get x = 3

Thus y = 9

Hence, option B is correct.

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 angle of intersection of the parabolas y² = 4 ax and x² = 4ay at the origin is

The angle of intersection of the curves y = 2 sin²x and y = cos² x at is