EQUATION OF TANGENTS AND NORMALS WORKSHEET

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

(i)  y  =  x²-4x-5, at x = -2       Solution

(ii)  y  =  x-sin x cos x, at x = π/2    Solution

(iii)  y  =  2sin²3x, at x = π/6      Solution

(iv)  y  =  (1+sin x)/cos x, at x  =  π/4     Solution

(2)  Find at what points on a circle

x²+y²  =  13

the tangent is parallel to the line 2x+3y = 7.

Solution

(3)  At what points on the curve

x²+y²-2x-4y+1  =  0

the tangent is parallel to

(i) x - axis   (ii) y - axis                Solution

(4)  Find the points on curve

x²-y²  =  2

at which the slope of the tangent is 2.     Solution

(5)  Find at what points on a circle

x²+y²  =  13

the slope of the tangent is -2/3.        Solution

(6)  Find the equations of those tangents to the circle

x² + y²  =  52

which are parallel to the straight line 2x+3y  =  6.

Solution

(7)  Find the equations of normal to

y  =  x³-3x

that is parallel to 2x+18y-9  =  0.         Solution

(8)  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

(9)  Prove that the curve

2x²+4y²  =  1 and 6x²-12y²  =  1

cut each other at right angles.        Solution

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