Question

The length of the latus rectum of the parabola \( x^2 + 2y = 8x - 7 \) is

• A. 8
• B. 2
• C. 6
• D. 4

Hint:

To find the length of the latus rectum, first rewrite the equation of the parabola in standard form and identify \( 4a \).

Answer 1

The Correct Option is B

Step 1: Write the equation in standard form.
The given equation is \( x^2 + 2y = 8x - 7 \). First, rearrange the equation to make it look like the standard form of a parabola: \[ x^2 - 8x + 2y + 7 = 0 \] Complete the square for \( x^2 - 8x \) to get: \[ (x - 4)^2 + 2y - 9 = 0 \] Now, the equation is in the form \( (x - h)^2 = 4a(y - k) \).
Step 2: Find the length of the latus rectum.
The length of the latus rectum for the parabola \( (x - h)^2 = 4a(y - k) \) is given by \( |4a| \). In this case, \( 4a = 2 \), so the length of the latus rectum is 2.
Step 3: Conclusion.
Thus, the correct answer is 2, corresponding to option (B).