assignment of tangent and normal

1. CHAPTER – 6
APPLICATION OF DERIVATIVES (TANGENTS AND NORMALS)
1. Findthe pointon the curve y = 2x2
+ 6x -4 at whichtangentisParallel to x – axis.
2. Findthe slope of the tangentto the curve y = x3
– x +1 at the pointwhere x- co-ordinate is2.
3. Determine the pointonthe curve y = 3x2
-1 at whichslope of tangentis3.
4. Findthe slope of the tangentto the curve y = 3x4
– 4x at x = 4.
5. Findthe slope of normal to the curve a𝒚 𝟐= 𝒙 𝟑 at (a𝒎 𝟐,a𝒎 𝟑)
6. At whatpointsonthe curve x2
+ y2
-2x -4y +1 = 0, the tangentsare parallel toy – axis? [(3,2)(-1,2)]
7. Findthe equationof tangenttothe curve y =
𝑋−7
( 𝑋−2)(𝑋−3)
at the pointwhere itcuts x-axis. [x-20y=7]
8. Show that the line
𝑥
𝑎
+
𝑦
𝑏
= 1 touchesthe curve y = be –x/a
at the pointwhere itcrossesthe y axis.
9. Findthe equationsof tangentandnormal to the curve x = 1-cos 𝜃, 𝑦 = 𝜃 − 𝑠𝑖𝑛 𝜃 𝑎𝑡 𝜃 =
𝜋
4
.
10. Findthe equationof the tangenttothe curve x2
+3y = 3, whichisparallel tothe line y – 4x + 5 =0.
11. Showthat the curves2x = y2
and2xy = K cut at rightanglesif K2
= 8.
12. Showthat the curves4x = y2
and4xy = K cut at rightanglesif K2
= 512 .
13. Findthe equationof tangentsandnormal to the parabolay2
= 4ax at (at2
,2at)
14. Showthat the curvesx = y2
and xy= K cut at right anglesif 8K2
= 1 .
15. Findthe equationof the tangenttothe curve y = √3𝑥 − 2 whichisparallel toline 4x - 2y + 5 = 0 .
16. Findall pointsonthe curve y = 4x3
– 2x5
at whichthe tangentspassesthroughthe origin.
17. Findthe equationof normal tothe curve y = x3
+ 2x + 6 whichare parallel toline x+14y+4=0.
18. Findthe pointsonthe curve y = x3
at whichthe slope of tangentisequal to y – coordinate of the point.
19. Showthat the line
𝑥
𝑎
+
𝑥
𝑏
= 1 touchesthe curve y = be –x/a
at the pointwhere the curve cutsy – axis.
20. Findthe equationof normal tothe curve x2
= 4y whichpassesthroughthe point(1,2)
21. Findthe equationof tangenttothe curve y= (𝒙 𝟑-1) (x-2) where the curve meetsthe x axis.
22. Findthe equationof normal at the point (a𝒎 𝟐,a𝒎 𝟑) for the curve a𝒚 𝟐= 𝒙 𝟑
23. Findthe equationof normal tothe curve 𝒚 𝟐 = 4x at (1,2)
24. Showthat the curves y = aex
and y = be –x
cut at rightanglesif ab = 1.
25. Findthe intervalsinwhichthe function f f(x) = x3
+
1
𝑥3
, x ≠ 0 isincreasingordecreasing.
26. Findthe equationof tangentandnormal to the curve x2/3
+ y2/3
= 2 at (1,1).
27. The equationof the tangentat (2, 3) on the curve y2
= ax3
+ b isy = 4x – 5. Findthe valuesof a and b.
28. Findthe equationof tangentline tothe curve y = x2
– 2x + 7 whichis
(i)Paralleltoline 2x – y + 9 = 0 (ii) Perpendiculartoline 5y – 15x = 13
29. Findthe value of x forwhich f(x) = [x(x – 2)]2
is an increasingfunction.Also,findthe pointsonthe curve,where
the tangentisparallel tox- axis.