Four Common Forms of Parabola Equation

Q.

If $z_1$ is rotated through an angle of ${120}^{\circ }$ anti-clockwise about $z_0$ to reach $z_2$ , then $\frac{z_2-z_0}{z_1-z_0}$ equal to

1. 

2. 

3. 

4. 

Q. The length of the latus rectum of the parabola $25\left[\right(x-2{)}^2+(y-4{)}^2]=(4x-3y+12{)}^2$ is

1. $\frac{16}{5}$
2. $\frac{4}{5}$
3. $\frac{8}{5}$
4. $\frac{12}{5}$

Q. An equilateral triangle is inscribed in the parabola $y^2=4ax$ such that one vertex of this triangle coincides with the vertex of the parabola. The length of side of this triangle is

1. $2a\sqrt{3}$
2. $4a\sqrt{3}$
3. $6a\sqrt{3}$
4. $8a\sqrt{3}$

Q.

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
$x^2=-9y$

Q. For the given parabola $x^2+2y=8x-7$ which of the following is/are correct?

1. axis will be $2y=9$
2. axis will be $x=4$
3. vertex will be $(4,\frac{9}{2})$
4. vertex will be $(\frac{9}{2},4)$

Q. The length of the latus rectum of the parabola $25\left[\right(x-2{)}^2+(y-4{)}^2]=(4x-3y+12{)}^2$ is

1. $\frac{16}{5}$
2. $\frac{12}{5}$
3. $\frac{8}{5}$
4. $\frac{4}{5}$

Q. Focus and directrix of the parabola $x^2=-8ay$ are

1. (0, -2a) and y = 2a
2. (0, 2a) and y = - 2a
3. (2a, 0)and x = - 2a
4. (-2a, 0) and x = 2a

Q. The equations $x=\frac{t}{4},y=\frac{t^2}{4}$ represents

1. A circle
2. A parabola
3. An ellipse
4. A hyperbola