Length of Subtangent

Q. The length of subtangent to the curve $\sqrt{x}+\sqrt{y}=3$ at the point(4, 1) is -

1. $\frac{1}{2}$
2. 2
3. $\frac{1}{3}$
4. 3

Q.

Find the length of subtangent on the curve y = $\frac{x}{1+x}$ where the slope of the tangent is $\frac{1}{9}$

[ The point where the tangent is drawn is in first quadrant ]

1. 6

Q.

[PT = length of tangent, $(x_1,y_1)$ is the point where the tangent is drawn, is the angle the tangent makes with x-axis, $x_1,y_1$, PT > 0]

How many of the following gives the length of subtangent ?

1. $\frac{y_1}{tan\theta }$
2. PT cos $\theta$
3. $\frac{y_1}{cot\theta }$
4. PT sin $\theta$

Q.

[PT = length of tangent, $(x_1,y_1)$ is the point where the tangent is drawn, is the angle the tangent makes with x-axis, $x_1,y_1$, PT > 0]

How many of the following gives the length of subtangent ?

1. $\frac{y_1}{tan\theta }$
2. PT cos $\theta$
3. $\frac{y_1}{cot\theta }$
4. PT sin $\theta$

Q. The length of subtangent to the curve $\sqrt{x}+\sqrt{y}=7$ at the point $(16,9)$ is

1. 4
2. 8
3. 12
4. 16

Q.

[PT = length of tangent, $(x_1,y_1)$ is the point where the tangent is drawn, is the angle the tangent makes with x-axis, $x_1,y_1$, PT > 0]

How many of the following gives the length of subtangent ?

1. $\frac{y_1}{tan\theta }$
2. PT cos $\theta$
3. $\frac{y_1}{cot\theta }$
4. PT sin $\theta$

Q.

Find the length of subtangent on the curve y = $\frac{x}{1+x}$ where the slope of the tangent is $\frac{1}{9}$

[ The point where the tangent is drawn is in first quadrant ]

1. 6

Q.

Length of subtangent is defined as the perpendicular distance between the point where the tangent is drawn and x-axis

1. True

2. False

Q.

Find the length of subtangent on the curve $y=\frac{x}{1+x}$, where the slope of the tangent is $\frac{1}{9}$

[ The point where the tangent is drawn is in first quadrant ]

___

Q. Match List-I with List-II and select the correct answer using the code given below. A B C D

List-I	List-II
a) Equation of tangent to the curve $y=b{e}^{-x/a}$ at $x=0$	1) $x-2y=2$
b) Equation of tangent to the curve $y=x^2+1$ at $(1,2)$	2) $y=2x$
c) Equation of normal to the curve $y=2x-x^2$at $(2,0)$	3) $x-y=\pi$
d) Equation of normal to the curve $y=\sin x$ at $x=\pi$	4) $\frac{x}{a}+\frac{y}{b}=1$

1. 4 1 2 3
2. 4 2 1 3
3. 1 4 3 2
4. 1 2 3 4

Q.

Length of subtangent is defined as the perpendicular distance between the point where the tangent is drawn and x-axis

1. False

2. True

Q.

Length of subtangent is defined as the perpendicular distance between the point where the tangent is drawn and x-axis

1. False

2. True

Q. Let$A=(1,2,3)$, $B=(3,4,5)$ then ?

1. Direction ratios of $AB$ line are $(2,2,2)$
2. Direction ratios of $\overline{AB}$ are $(-1,1,-1)$
3. Direction ratios of $\overline{AB}$ are $(1,1,1)$
4. Direction cosine od $AB$ line may be $(\frac{1}{\sqrt{3}}-\frac{1}{\sqrt{3}}-\frac{1}{\sqrt{3}})$

Q. Find the distance of the point $P(1,-3)$ from the line $2y-3x=4$.

Q. Length of subtangent is defined as the length of projection of tangent between the points where the tangent is drawn and the point where the tangent meets x-axis.

1. False
2. True