Focus

Q.

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

1. $(\frac{3}{2},\frac{-1}{2})$

2. $(1,\frac{-1}{2})$

3. $1,0$

4. $0,1$

Q. If the focus of the parabola $x^2-ky+3=0$ is $(0,2)$, then the value(s) of $k$ is/are

1. $4$
2. $6$
3. $3$
4. $2$

Q.

The latus rectum of parabola $y^2=5x+4y+1$ is

1. $\frac{5}{4}$

2. $10$

3. $5$

4. $\frac{5}{2}$

Q. The coordinates of focus of parabola $9y^2-9x-12y-57=0$ is

1. $(-\frac{235}{36},-\frac{2}{3})$
2. $(-\frac{235}{36},\frac{2}{3})$
3. $(\frac{235}{36},\frac{2}{3})$
4. $(\frac{235}{36},-\frac{2}{3})$

Q. Co-ordinate of the focus of the parabola $x^2-4x-8y-4=0$ are

1. $0,2$
2. $2,1$
3. $(-3,\frac{-71}{10})$
4. $2,-1$

Q. The parabola $y^2=px$ passes through the point of intersection of lines $\frac{x}{3}+\frac{y}{2}=1$ and $\frac{x}{2}+\frac{y}{3}=1$ its focus is

1. $(\frac{3}{10},0)$
2. $(\frac{3}{5},0)$
3. $(\frac{3}{7},0)$
4. $(\frac{6}{7},0)$

Q. The equation of reflection of $y^2=x$ about $y-$axis is

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

Q. The coordinates of the focus of the parabola described parametrically by $x=5t^2+2$ and $y=10t+4$ are

1. $(7,4)$
2. $(3,4)$
3. $(3,-4)$
4. $(-7,4)$

Q. Co-ordinate of the focus of the parabola $x^2-4x-8y-4=0$ are

1. $0,2$
2. $2,1$
3. $(-3,\frac{-71}{10})$
4. $2,-1$

Q. If the focus of the parabola $x^2-ky+3=0$ is $(0,2)$, then the value(s) of $k$ is/are

1. $4$
2. $6$
3. $3$
4. $2$