Focus

Q. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Q.

The focus and vertex of a parabola are (4, 5) and (3, 6). The equation of axis is

1. 2x-y+3=0

2. 2x-y=0

3. 2x+y-13=0

4. x+y-9=0

Q.

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
$y^2=10x$

Q. If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

Q. Find the coordinates of the focus axis of the parabola, the equation of directrix and the length of the latus rectum for the parabola $x{}^2$ $=-16y$.

Q. IF $A$ be a square matrix, then $A+A^T$ is a symmetric matrix ?

1. True
2. False

Q. Let $P$ be the point $(1,0)$ and $Q$ be a point on the curve $y^2=8x$. Then the locus of the mid-point of $PQ$ is

1. $y^2+4x+2=0$
2. $y^2-4x+2=0$
3. $x^2-4y+2=0$
4. $x^2+4y+2=0$

Q. Find the equation of the hyperbola satisfying the give conditions: Foci $(0,\pm 13)$ the conjugate axis is of length $24$

Q. The focus of the parabola $y^2=4y-4x$ is

1. (0, 2)
2. (1, 2)
3. (2, 0)
4. (2, 1)

Q. Find the coordinates of the focus axis of the parabola the equation of directrix and the length of the latus rectum for $y{}^2$$=-8x$

Q. The end points of the latus rectum of a parabola having vertex at origin are $(4,8)$ and $(4,-8)$ then the equation of the parabola is

1. $y^2=4x$
2. $y^2=8x$
3. $y^2=16x$
4. $x^2=8y$