JEE Main 2024 Mathematics question
Let the line L : pass through the point of the intersection P (in the first quadrant) of the circle and the parabola . Let the line L touch two circles and of equal radius . If the centres and of the circles and lie on the y-axis, then the square of the area of the triangle is equal to.
Answer: 72
Solution
P = (√2, 1), α = 3; tangency gives |k − 3|/√3 = 2√3 so centres (0, 9) and (0, −3); area = ½ × 12 × √2 = 6√2, whose square is 72.