Home
Class 12
MATHS
The lengths of tangent, subtangent, norm...

The lengths of tangent, subtangent, normal and subnormal for the curve ` y=x^(2)+x-1 ` at (1,1) are A,B,C and D respectively, then their increasing order is

A

B,D,A,C

B

B,A,C,D

C

A,B,C,D

D

B,A,D,C

Text Solution

Verified by Experts

The correct Answer is:
D
The equation of the curve is `y=x^(2)+x-1.`
` therefore (dy)/(dx) =2x+1 rArr ((dy)/(dx))_((1","1)) =3 `
Now ,
A=Length of the tangent at (1,1)
` rArr A=(sqrt(1+((dy)/(dx))^(2)))/((dy)/(dx))=(sqrt(1+3^(2)))/(3) =(sqrt(10))/(3) `
B= Length of the subtangent at (1,1)
` B=(y)/((dx)/(dy))=(1)/(3) `
C=Length of the normal at (1,1)
` rArr C=sqrt(1+((dy)/(dx))^(2))=sqrt(1+3^(2))=sqrt(10) `
D=Length of the subnormal at (1,1)
` rArr D=y(dy)/(dx)=1 xx 3 =3 `
Thus, we have `B lt A lt D lt C .`
Promotional Banner

Similar Questions

Explore conceptually related problems

Length of tangent; normal; subtangent and subnormal

Length OF tangent, Normal Subtangent and Subnormal

The length of the subtangent at any point (x_1,y_1) on the curve y=5^x is

Find the equation of tangent and normal to the curve 2y=3-x^(2) at (1, 1).

Slope of the normal to the curve y=2x^(2)-1 at (1, 1) is …………… .

Find the slopes of the tangent and the normal to the curve x y=6 at (1,\ 6)

If x=y is a tangent to the curve y=x^(2)+bx+c at (1,1) then

Equation of the tangent and normal to the curve x^(5)+y^(5)=2xy at the point (1, 1) are respectively.