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If the parabola y^2=4a x\ passes throug...

If the parabola `y^2=4a x\ ` passes through the point (3,2) then find the length of its latus rectum.

A

`2/3`

B

`4/3`

C

`1/3`

D

4

Text Solution

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The correct Answer is:
To solve the problem, we need to find the length of the latus rectum of the parabola given by the equation \(y^2 = 4ax\) that passes through the point (3, 2). ### Step-by-step Solution: 1. **Identify the equation of the parabola**: The equation of the parabola is given as \(y^2 = 4ax\). 2. **Substitute the point into the equation**: Since the parabola passes through the point (3, 2), we substitute \(x = 3\) and \(y = 2\) into the equation: \[ 2^2 = 4a \cdot 3 \] 3. **Calculate the left-hand side**: Calculate \(2^2\): \[ 4 = 4a \cdot 3 \] 4. **Simplify the equation**: Now we can simplify the equation: \[ 4 = 12a \] 5. **Solve for \(a\)**: To find \(a\), divide both sides by 12: \[ a = \frac{4}{12} = \frac{1}{3} \] 6. **Find the length of the latus rectum**: The length of the latus rectum of a parabola is given by the formula \(4a\). Now substitute the value of \(a\): \[ \text{Length of latus rectum} = 4a = 4 \cdot \frac{1}{3} = \frac{4}{3} \] 7. **Final answer**: Therefore, the length of the latus rectum is \(\frac{4}{3}\).

To solve the problem, we need to find the length of the latus rectum of the parabola given by the equation \(y^2 = 4ax\) that passes through the point (3, 2). ### Step-by-step Solution: 1. **Identify the equation of the parabola**: The equation of the parabola is given as \(y^2 = 4ax\). 2. **Substitute the point into the equation**: ...
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