(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.
(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.
(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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