Show that the equation of normal at any point t on the curve x = 3 cos t – cos³t and y = 3 sin t – sin³t is 4(y cos2t – x sin³t) = 3 sin 4t
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 and normal to the curve x = 1 – cos θ, y = θ – sin θ at θ =
Find the points on the curve y = x³ at which the slope of the tangent is equal to y-coordinate of the point.
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 y = x³ – 3x² – 9x + 7 at which the tangent to the curve is parallel to the x-axis.
The equation of tangent at (2, 3) on the curve y² = ax³ + b is y = 4x – 5. Find the values of a and b.
Find the equation of the normal at a point on the curve x² = 4y which passes through the point (1, 2). Also find the equation of the corresponding tangent.
Find the value of p for which the curves x² = 9p(9 – y) and x² = p(y + 1) cut each other at right angles.
Show that the relation R in the Set A = {1, 2, 3, 4,5} given by R = {(a, b) : |a – b| is divisible by 2} is an equivalence relation. Write all the equivalence classes of R.
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 equations of tangents to the curve 3x² – y² = 8, which passes through the point