
6-56 Calculus – Differentiation and Integration
8. Show that the normal to the curve 5x
5
- 10x
3
+ x
2
y + 6 = 0 at (0, -3) is also a tangent at two
other points of the curve.
9. Find the equations of three normals to the curve y = x
2
that passes through the point (0, 3/2).
Find the angle between the pairs:
10. y = sin x, y = cos x.
11. 2y
2
= x
3
, y
2
= 32x.
12. y
2
= ax, x
3
+ y
3
= 3axy.
13. y
2
= 4ax, x
2
= 4by.
14. Prove that the curves x
3
+ 2xy
2
- 10a
2
x + 12a
2
y + 3a
3
= 0 and y
3
+ 2xy
2
- 5a
2
x - a
3
= 0
intersect at an angle tan
-1
(88/73) at the point (3a, -2a).
Find the lengths of tangent, sub-tangent, normal and sub-normal to the following curves: ...