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.

Answer 2

For the parabola $ x^2 = 4ay $, the general formula for the length of the latus rectum is $ 4a $. 

Given that the parabola passes through the point $ (2, 1) $, we substitute these values into the equation of the parabola: $$ x^2 = 4ay $$ Substituting $ x = 2 $ and $ y = 1 $: $$ 2^2 = 4a(1) $$ $$ 4 = 4a $$ $$ a = 1 $$ Now, the length of the latus rectum is given by $ 4a $, so: $$ \text{Length of the latus rectum} = 4(1) = 4 $$  The length of the latus rectum is 4.