Question

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

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

• A. P - V, Q - U, R - T, S - W
• B. P - T, Q - U, R - V, S - W
• C. P - U, Q - V, R - T, S - W
• D. P - V, Q - U, R - W, S - T

Answer 1

The correct option is A

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

P) Focal distance: As the name suggests it is the distance of a point on parabola from the focus. But since the eccentricity of parabola is one, $\frac{PS}{PM}=e=1\Rightarrow PS=PM$ or the distance from focus is equal to distance from directrix.

Q) Double ordinate is a chord of parabola perpendicular to axis or in this case x-axis

R) Latus rectum is a chord of the parabola perpendicular to axis and passing through focus. It is the line x = a in this case

S) Vertex of the parabola is the meeting point of axis and parabola. It is origin in this case.