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JEE Main 202529 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Parabola

JEE Main 2025 · 29 January · Morning Shift · Mathematics · Parabola

Two parabolas have the same focus (4,3) and their directrices are...

Two parabolas have the same focus (4,3)(4,3) and their directrices are the xx-axis and the yy-axis, respectively. If these parabolas intersects at the points AA and BB, then (AB)2(A B)^2 is equal to :

Options

  1. A392
  2. B384
  3. C192
  4. D96

Correct answer

C. 192

Step-by-step solution

The parabolas are (x−4)2+(y−3)2=x2(x-4)^2+(y-3)^2=x^2 ...(i)and(x−4)2+(y−3)2=y2and (x-4)^2+(y-3)^2=y^2... If point of intersection are A(x1,y1)A\left(x_1, y_1\right) and B(x2,y2)B\left(x_2, y_2\right) By solving (i) and (ii), we get x1+x2=14 and x1x2=25(AB)2=2((x1+x2)2−4x1x2)=192\begin{aligned} & x_1+x_2=14 \text{ and } x_1 x_2=25 \\ & (A B)^2=2\left(\left(x_1+x_2\right)^2-4 x_1 x_2\right)=192 \end{aligned}
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