Projection of a Line

Q. For any point on the curve $x=4a(t^2-{\cos }^{2}t),y=a(t^2+{\sin }^{2}t),$ which of the following(s) is(are) correct

1. Length of sub-tangent $=4y$
2. Length of sub-normal $=4y$
3. Length of sub-normal $=\frac{y}{4}$
4. Length of sub-tangent $=\frac{y}{4}$

Q. The graph of the curve $y=\frac{(x^2+1)}{(x^2-1)}$ is:

1. 
2. 
3. 
4. 

Q. If the area of the triangle formed by the positive $x-$axis, the normal and the tangent to the circle $(x-2{)}^2+(y-3{)}^2=25$ at the point $(5,7)$ is $A,$ then $24A$ is equal to

Q.

Let $P\left(x\right)=x^4+a{x}^3+b{x}^2+cx+d$ such that $x=0$ is the only real root of $P\left(x\right)=0$. If $P(-1)<P\left(1\right),$ then in the interval $[-1,1]$

1. $P(-1)$ is the minimum and $P\left(1\right)$ is the maximum of $P$

2. $P(-1)$ is not minimum but $P\left(1\right)$ is the maximum of $P$

3. $P(-1)$ is minimum and is not maximum of $P$

4. Neither $P(-1)$ is the minimum and$P\left(1\right)$ nor is the maximum of$P$

Q. For the function $y=\frac{1}{1+x^2}$, which of the following is/are correct:

1. It has a horizontal asymptote.
2. It is symmetric about $x=0$
3. It is increasing $\forall x\in R$
4. It has maxima at $x=0$

Q. For any point on the curve $x=4a(t^2-{\cos }^{2}t),y=a(t^2+{\sin }^{2}t),$ which of the following(s) is(are) correct

Q. The graph of the function $f\left(x\right)=x^2+\frac{1}{x}$ is:

1. 
2. 
3. 
4. 

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. The number of asymptotes of the curve given by $2xy+4x-6y+17=0$ is equal to

Q. The number of asymptotes of the curve $y=\frac{7-x^2}{7+x^2}$ is

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