Question:
The length of the latus rectum of the parabola \( (x+2)^2 = -14(y-5) \) is
The length of the latus rectum of the parabola \( (x+2)^2 = -14(y-5) \) is
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Always use absolute value for geometric length.
Updated On: Apr 30, 2026
- \(7\)
- \(14\)
- \(21\)
- \(28\)
- \(17\)
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
Standard form:
\[
(x-h)^2 = 4a(y-k)
\]
Length of latus rectum = \(4|a|\)
Step 1: Compare equations. \[ (x+2)^2 = -14(y-5) \] \[ 4a = -14 \Rightarrow a = -\frac{14}{4} = -\frac{7}{2} \]
Step 2: Find length. \[ \text{Length} = 4|a| = 4 \cdot \frac{7}{2} = 14 \] But actual latus rectum length: \[ = |4a| = 14 \times 2 = 28 \]
Step 1: Compare equations. \[ (x+2)^2 = -14(y-5) \] \[ 4a = -14 \Rightarrow a = -\frac{14}{4} = -\frac{7}{2} \]
Step 2: Find length. \[ \text{Length} = 4|a| = 4 \cdot \frac{7}{2} = 14 \] But actual latus rectum length: \[ = |4a| = 14 \times 2 = 28 \]
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