Find the equations of the normal to the curve y = 4x³ – 3x + 5 which are perpendicular to the line 9x – y + 5 = 0..
Find the equation of tangent to the curve x² + 3y = 3, which is parallel to line y – 4x + 5 = 0.
Find the equation of tangents to the curve y = x³ + 2x – 4 which are perpendicular to the line x + 14y – 3 = 0.
Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).
Find the equation of the tangent to the curve y = x⁴ – 6x³ + 13x² – 10x + 5 at point x = 1, y = 0.
Find the equation of tangent to the curve y = cos (x + y), -2π ≤ x ≤ 0, that is parallel to the line x + 2y = 0.
Find the equation of tangent to the curve 4x² + 9y² = 36 at the point (3 cos θ, 2 sin ).
Show that the relation R on the set Z of all integers defined by (x, y) ∈ is divisible by 3 is an equivalence relation.
Find a vector of magnitude 5 units and parallel to the resultant of = and = .
Find the particular solution of the differential equation given that y = 0 when x = 1.
Find the equations of tangents to the curve y = (x²– 1) (x – 2) at the points, where the curve cuts the X-axis.
Prove that x² – y² = c(x² + y²)² is the general solution of the differential equation (x² – 3xy²) dx = (y³ – 3x²y) dy, where C is a parameter.