Parametric Representation: Hyperbola

Q. Total number of solutions of the equation $3x+2\tan x=\frac{5\pi }{2}$ in $\in [0,2\pi ],$ is equal to

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

Q.

If a triangle is inscribed in a rectangular hyperbola, its orthocentre lies

1. inside the curve

2. Outside the curve

3. on the curve

4. none of these

Q.

The parametric form the curve
$\frac{(x+1{)}^2}{16}-\frac{(y-2{)}^2}{4}=1$ is

1. $(4\sec \theta ,2\tan \theta )$

2. $(4\sec \theta +1,2\tan \theta -2)$

3. $(4\sec \theta -1,2\tan \theta +2)$

4. $(4\sec \theta -4,2\tan \theta -2)$

Q.

A conic section is defined by the equations x = - 1 + sect y = 2 + z tant. The coordinates of the foci are,

1. $(-1-\sqrt{10},2)and(-1+\sqrt{10},2)$

2. $(-1-\sqrt{8},2)and(-1+\sqrt{8},2)$

3. $(-1,2-\sqrt{8})and(-1,2+\sqrt{8})$

4. $(-1,2-\sqrt{10})and(-1,2+\sqrt{10})$

Q.

What is the equation of a curve given by the parametric form $x=9+6sec\theta ;y=-2-4tan\theta$.

1. $\frac{(x+9{)}^2}{36}-\frac{(y-2{)}^2}{16}=1$

2. $\frac{(x-9{)}^2}{36}-\frac{(y+2{)}^2}{16}=1$

3. $\frac{(x-6{)}^2}{81}-\frac{(y+4{)}^2}{4}=1$

4. $\frac{(x+6{)}^2}{81}-\frac{(y-4{)}^2}{4}=1$