Question:
If the parabola \(y^2=4ax\) passes through the point \((3,2)\), then the length of its latus rectum is:
If the parabola \(y^2=4ax\) passes through the point \((3,2)\), then the length of its latus rectum is:
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For \(y^2=4ax\), the length of latus rectum is always \(4a\).
Updated On: May 7, 2026
- \(\frac{4}{3}\)
- \(4\)
- \(\frac{2}{3}\)
- \(\frac{1}{3}\)
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The Correct Option is A
Solution and Explanation
Concept:
For the parabola:
\[
y^2=4ax
\]
the length of the latus rectum is:
\[
4a
\]
Step 1: Given parabola: \[ y^2=4ax \] It passes through the point: \[ (3,2) \]
Step 2: Substitute \(x=3\) and \(y=2\). \[ 2^2=4a(3) \] \[ 4=12a \] \[ a=\frac{1}{3} \]
Step 3: Length of latus rectum is: \[ 4a \] \[ 4a=4\left(\frac{1}{3}\right) \] \[ 4a=\frac{4}{3} \] Therefore, \[ \boxed{\frac{4}{3}} \]
Step 1: Given parabola: \[ y^2=4ax \] It passes through the point: \[ (3,2) \]
Step 2: Substitute \(x=3\) and \(y=2\). \[ 2^2=4a(3) \] \[ 4=12a \] \[ a=\frac{1}{3} \]
Step 3: Length of latus rectum is: \[ 4a \] \[ 4a=4\left(\frac{1}{3}\right) \] \[ 4a=\frac{4}{3} \] Therefore, \[ \boxed{\frac{4}{3}} \]
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