Question

If the parabola x² = 4ay passes through the point (2, 1), then the length of the latus rectum is

• A. 1
• B. 4
• C. 2
• D. 8

Answer 1

The Correct Option is B

If the parabola \(x^2 = 4ay\) passes through the point (2, 1), then we need to find the length of the latus rectum.

Since the point (2, 1) lies on the parabola \(x^2 = 4ay\), we can substitute x = 2 and y = 1 into the equation:

\(2^2 = 4a(1)\)

\(4 = 4a\)

\(a = 1\)

The length of the latus rectum for a parabola in the form \(x^2 = 4ay\) is given by \(4a\).

Since \(a = 1\), the length of the latus rectum is \(4(1) = 4\).

Therefore, the correct option is (B) 4.