Conic Sections
Conic Section
Allen Star Batch
Grade 11
Question:
'$O'$ is the vertex of parabola $y^2 = 4x$ and $L$ is the upper end of latus rectum. If $LH$ is drawn perpendicular to $OL$ meeting $x$-axis in $H$, then length of double ordinate through $H$ is $\sqrt{N}$, then $N =$
Step-by-Step Solution
Key Concept: The length of a double ordinate (latus rectum) at a point on a parabola is $4r'$ where $r'$ is the focal distance.
Starting with $\frac{0-2}{x-1} = -\frac{1}{2}$, solve to get $x = 5$. Then $r^2 = 5$ gives $r' = \sqrt{5}$. The length of double ordinate is $4r' = 4\sqrt{5} = \sqrt{80}$, so $N = 80$.
Correct Answer: 80