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 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 line to the curve y =x² -2x + 7 which is
(i) parallel to the line 2x-y +9 =0
(ii) perpendicular to the line 5y - 15x = 13.
Find the equation of the tangent to the curve which is parallel to the line 4x – 2y + 5 = 0.
Prove that the curves x = y² and xy = k cut at right angles if 8k² = 1.
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 equations of tangents to the curve 3x² – y² = 8, which passes through the point
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.
Find the angle of intersection of the curves y² = 4ax and x²= 4by.
Find the value of p for which the curves x² = 9p(9 – y) and x² = p(y + 1) cut each other at right angles.
Find the equation of tangent and normal to the curve x = 1 – cos θ, y = θ – sin θ at θ =
Using derivative, find the approximate percentage increase in the area of a circle if its radius is increased by 2%.
If x changes from 4 to 4·01, then find the approximate change in log x.
Using differentials, find the approximate value of