Focal Distance

Q. Consider the parabola $X^2+4Y=0$. Let p = (a, b) be any fixed point inside the parabola and let 'S' be the focus of the parabola. Then the minimum value SQ + PQ as point Q moves on the parabola is

1. $|1-a|$
2. $\left|ab\right|+1$
3. $\sqrt{a^2+b^2}$
4. $1-b$

Q. The focal distance of the point (9, 6) on the parabola $y^2=4x$ is

1. 4
2. 8
3. 10
4. 16

Q.

Match the following. Equation of the parabola is $y^2=4ax$

$\begin{array}{cc}\text{Column 1}& \text{Column 2}\\ \text{P) Focal distance}& \text{T) Focal chord perpendicular to axis}\\ \text{Q) Double ordinate}& \text{U) A chord perpendicular to axis}\\ \text{R) Latus rectum}& \text{V) Distance of a point on parabola from directrix}\\ \text{S) Vertex}& \text{W) Meeting point of axis and parabola}\end{array}$

1. P - V, Q - U, R - T, S - W

2. P - T, Q - U, R - V, S - W

3. P - U, Q - V, R - T, S - W

4. P - V, Q - U, R - W, S - T

Q. The focal distance of a point on the parabola $y^2=16x$ whose ordinate is twice the abscissa, is

1. 6
2. 8
3. 10
4. 12

Q. The co-ordinates of a point on the parabola $y^2=8x$ whose focal distance is 4 is

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