Find the slope of tangent to the curve y = 3x² – 6 at the point on it whose x-coordinate is 2.
Find the points on the curve x² + y² – 2x – 3 = 0 at which tangent is parallel to x-axis.
Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).
Find the equation of tangent to the curve 4x² + 9y² = 36 at the point (3 cos θ, 2 sin ).
Find the angle of intersection of the curves x² + y² = 4 and (x – 2)² + y²= 4, at the point in the first quadrant.
Find the equation of the tangent to the curve y = x⁴ – 6x³ + 13x² – 10x + 5 at point x = 1, y = 0.
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.
In a hockey match, both teams A and B scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not.
Find the equation of tangent and normal to the curve x = 1 – cos θ, y = θ – sin θ at θ =
Find the angle of intersection of the curves y² = 4ax and x²= 4by.
Obtain the differential equation of all the circles of radius r.
Show that the normal at any point θ to the curve x = a cos θ + aθ sin θ, y = a sin θ – aθ cos θ is at a constant distance from the origin.