Question:
The directrix of a parabola is $x + 8 = 0$ and its focus is at $(4, 3)$. Then the length of the latus-rectum of the parabola is:
The directrix of a parabola is $x + 8 = 0$ and its focus is at $(4, 3)$. Then the length of the latus-rectum of the parabola is:
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Shortcut: Distance (focus to directrix) = \( 2a \).
So, latus rectum = \( 2 \times \text{distance} \).
Updated On: May 2, 2026
- $5$
- $9$
- $10$
- $12$
- $24$
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The Correct Option is
Solution and Explanation
Concept:
For a parabola:
\[
\text{Distance between focus and directrix} = 2a
\]
and
\[
\text{Length of latus rectum} = 4a
\]
Step 1: Find distance between focus and directrix.
Focus \( S(4,3) \), Directrix \( x = -8 \) Distance: \[ d = |4 - (-8)| = 12 \]
Step 2: Relate with parameter \( a \).
\[ 2a = 12 \Rightarrow a = 6 \]
Step 3: Find length of latus rectum.
\[ \text{Length} = 4a = 4 \times 6 = 24 \]
Step 4: Final answer.
\[ \boxed{24} \]
Step 1: Find distance between focus and directrix.
Focus \( S(4,3) \), Directrix \( x = -8 \) Distance: \[ d = |4 - (-8)| = 12 \]
Step 2: Relate with parameter \( a \).
\[ 2a = 12 \Rightarrow a = 6 \]
Step 3: Find length of latus rectum.
\[ \text{Length} = 4a = 4 \times 6 = 24 \]
Step 4: Final answer.
\[ \boxed{24} \]
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