JEE Main 2024 Mathematics question
Let L₁, L₂ be the lines passing through the point P(0, 1) and touching the parabola 9x² + 12x + 18y − 14 = 0. Let Q and R be the points on the lines L₁ and L₂ such that the ΔPQR is an isosceles triangle with base QR. If the slopes of the lines QR are m₁ and m₂. then 16(m₁² + m₂²) is equal to .
Answer: 68
Solution
Substituting y = mx + 1 in the parabola gives 9x² + (18m + 12)x + 4 = 0; tangency needs (18m + 12)² = 144, so the tangents have slopes 0 and −4/3. For PQR isosceles with
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