Question

If the parabola $y^{2} = 4ax$ passes through the point (3, 2) then the length of its latus rectum is:}

• A. $4/3$
• B. 4
• C. $2/3$
• D. $1/3$

Hint:

Don't solve for '$a$' unless you have to; the question asks for '$4a$', which you can often isolate directly.

Answer 1

The Correct Option is A

Step 1: Concept
The length of the latus rectum for the parabola $y^{2} = 4ax$ is defined as $4a$.

Step 2: Meaning
Since the point $(3, 2)$ lies on the parabola, it must satisfy the equation $y^{2} = 4ax$.

Step 3: Analysis
Substitute $x = 3$ and $y = 2$: $2^{2} = 4a(3) \implies 4 = 12a$. Dividing both sides by 3 gives $4/3 = 4a$.

Step 4: Conclusion
The length of the latus rectum $4a$ is therefore $4/3$.
Final Answer: (A)