Find the points on the curve x² + y² – 2x – 3 = 0 at which tangent is parallel to x-axis.
Find the point on the curve y = x³ – 11x + 5 at which the equation of tangent is y = x – 11.
Find the equation of tangent and normal to the curve x = 1 – cos θ, y = θ – sin θ at θ =
Prove that the curves x = y² and xy = k cut at right angles if 8k² = 1.
If A and B are two independent events such that P(A' ∩ B)= 2/15 and P(A ∩ B')= 1/6, then find P(A) and P(B).
Obtain the differential equation of all the circles of radius r.
Show that the function f : R {x ∈ R – 1 < x < 1} defined by f(x) = x ∈ R is one-one and onto function. Hence find f⁻¹(x).
Consider given by f(x) = Show that f is bijective. Find the inverse of f and hence find f⁻¹(0) and x such that f⁻¹(x) = 2.
Find the equations of tangents to the curve 3x² – y² = 8, which passes through the point