SARADA EDUCATIONAL INSTITUTIONS
MOGHALRAJAPURAM, VIJAYAWADA
JR INTER
IMPORTANT QUESTIONS UT-4
MATHS-1B
SAQ’S
TANGENTS & NORMALS -4MARKS
1. Find the equations of tangent and normal to the curve y=x 3+4x2 at (-1,3)
2. Find the equations of tangent and normal to the curve xy=10 at (2,5)
3. Find the equations of normal to the curve y=x2-4x+2 at (4,2)
4. Find the equation of the normal to the curve y=5x4 at the point(1,5)
n n
x y x y
5. For the curve 2 Show that tangent at (a, b) is 2
a b a b
6. Show that at any point (x,y) on the curve y=bex/a,the length of the sub- tangent is a constant.
7. Show that the length of the subtangent at any point on the curve y=ax(a>0) is a constant
8. Show that the length of the subnormal at any point on the curve y2=4ax is a constant.
a ax ax
9. Find the length of normal and length of the sub-normal for the curve y 2 e e
x
10. Find the length of the subtangent and sub normal of the curve y b sin
a
LAQ’S
TANGENTS AND NORMALS(7M)
1. Show that the tangent on the curve x y a at the point P( x 1 , y1 ) is
1 1 1
xx 1
2
yy1
2
a 2
2 2 2
2. If the tangent at any point on the curve x 3 y 3 a 3 intersects the coordinate axes in
A and B, then show that the length AB is a constant.
3. If the tangent at any point P on the curve x m y n am n (m n 0) meets the coordinate
axes in A, B, then show that AP : PB is a constant.
4. Find the angle between the curves 2y2-9x=0, 3x2+4y=0 (in the 4th quqdrant)
5. Find the angle between the curves xy=2, and x2+4y=0
6. Find the angle between the curves y 2 4 x ; x 2 y 2 5 .
7. Show that the curves y 2 4( x 1) and y 2 36(9 x ) intersect orthogonally..
1 1
8. Show that the curves 6 x 2 5 x 2 y 0 and 4 x 2 8 y 2 3 touch each other at , .
2 2
9. 2 2
Find the angle between the curves y = 8x , 4x + y = 32 2
DIFFERENTIATION(7M)
dy y 1 log x log y
10. If x log y log x then show that dx x log 2 x
.
dy y ( x log y y)
11. If x y y x then show that dx x (y log x x ) .
dy yx y 1 y x log y
12. If x y a then show that dx y
x log x xy x 1 .
y x b
dy 1 y2
13. If 1 x 1 y a( x y ) , then show that
2 2
dx 1 x2
dy y2 y2
14. If y=xy then show that =
dx x 1 log y x 1 y log x
dy log x
15. If x e x y , then show that =
dx 1 log x
y 2
