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: Understanding the Concept:
A point lies on a curve if its coordinates satisfy the equation of the curve. For a parabola \(y^2 = 4ax\), the length of the latus rectum is the coefficient of \(x\), which is \(4a\).
Step 2: Key Formula or Approach:
1. Substitute the point into the equation to find \(a\) or \(4a\).
2. Length of latus rectum = \(4a\).
Step 3: Detailed Explanation:
The parabola \( y^2 = 4ax \) passes through \((3, 2)\). Substitute \(x = 3\) and \(y = 2\): \[ (2)^2 = 4a(3) \] \[ 4 = 12a \] Divide both sides by 3 to isolate \(4a\): \[ 4a = \frac{4}{3} \] Since the length of the latus rectum is \(4a\), we have: \[ \text{Latus Rectum} = \frac{4}{3} \]
Step 4: Final Answer:
The length of the latus rectum is \( 4/3 \).