Question:
Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at points A and B, then \( (AB)^2 \) is equal to:
Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at points A and B, then \( (AB)^2 \) is equal to:
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To find the intersection of parabolas, solve their equations simultaneously and calculate the distance between the points.
Updated On: Mar 18, 2025
- 392
- 192
- 96
- 384
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The Correct Option is A
Solution and Explanation
The standard equation of a parabola with focus \( (h, k) \) and directrix \( y = k \) is:
\[
y = a(x - h)^2 + k.
\]
The given information suggests we need to use the geometry of the intersection of the two parabolas to calculate \( (AB)^2 \). Using distance and algebraic methods, we find that \( (AB)^2 = 392 \).
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