Tangent and Normal Worksheet





In this page tangent and normal worksheet we are going to some practice question of the concept equation of tangent and equation of normal. For each question you can find solution.

(1) Find the equation of the tangent and normal of the following curves

(i) y = x² - 4 x - 5, at x = -2

Solution

(ii) y = x - sin x cos x, at x = π/2

Solution

(iii) y = 2 sin ² 3 x, at x = π/6

Solution

(iv) y = (1+sin x)/cos x,at x = π/4

Solution

(2) Find the points on curve x² - y² = 2 at which the slope of the tangent is 2.

Solution

(3) Find at what points on a circle x² + y² = 13, the tangent is parallel to the line 2x + 3 y = 7.

Solution

(4) At what points on the curve x²+y²-2x-4y+1 = 0 the tangent is parallel to

(i) x - axis   (ii) y - axis

Solution

(5) Find the equations of those tangents to the circle x² + y² = 52, which are parallel to the straight line 2 x + 3 y = 6.

Solution

(6) Find the equations of normal to y = x³ - 3 x that is parallel to 2 x + 18 y - 9 = 0.

Solution

(7) Let P be a point on the curve y = x³ and suppose that the tangent line at P intersects the curve again at Q. Prove that the slope at Q is four times the slope at P.

Solution

(8) Prove that the curve 2x²+4y²=1 and 6x²-12y²=1 cut each other at right angles. 

Solution

(9) At what angle θ do the curve y = a^x and y = b^x intersect (a ≠ b)?

(10) Show that the equation of the normal to the curve x = a cos³ θ, y = a sin³ θ at "θ" is x cos θ - y sin θ = a cos 2 θ

(11) If the curve y² = x and x y = k are orthogonal then prove that 8 k² = 1

tangent and normal worksheet