Question

One of the tangents at the end of the latus rectum of the parabola \(y^{2}=12x\) is

• A. \(x-y+3=0\)
• B. \(2x+y=0\)
• C. \(3x+y-3=0\)
• D. \(x+3y-3=0\)

Hint:

The ends of the latus rectum of y squared = 12x are (3, 6) and (3, -6).

Answer 1

The Correct Option is A

Step 1: Use the slope form
A tangent to $y^2=4ax$ is $y=mx+\dfrac am$. Here $a=3$.

Step 2: Use the end point
At $(3,6)$: $6=3m+\dfrac3m\Rightarrow m^2-2m+1=0\Rightarrow m=1$.

Step 3: Write the line
$y=x+3$, which is $x-y+3=0$.

Final Answer:
The slope form also gives x minus y plus 3 equals 0. \[ \boxed{\text{(A) }x-y+3=0} \]