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 y = 4x³ – 3x + 5 which are perpendicular to the line 9x – y + 5 = 0..
Find the equations of the normal to the curve y = x³+ 2x + 6, which are parallel to line x + 14y + 4 = 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 tangent to the curve y = cos (x + y), -2π ≤ x ≤ 0, that is parallel to the line x + 2y = 0.
Find the equation(s) of the tangent(s) to the curve y = (x³ – 1) (x – 2) points where the curve intersects the x-axis.
Find the equations of tangents to the curve y = (x²– 1) (x – 2) at the points, where the curve cuts the X-axis.
Find the angle of intersection of the curves y² = 4ax and x²= 4by.
Solve the differential equation x cos x + sin x, given that y = 1 when
Prove that the curves x = y² and xy = k cut at right angles if 8k² = 1.
LetA = {x ∈ Z:0≤ x ≤12}. Show that R={(a,b):a,b ∈ A, |a-b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2].
Find the particular solution of the differential equation given that when x = 0, y = 0.
Find the equation of tangent and normal to the curve x = 1 – cos θ, y = θ – sin θ at θ =