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() is equal to___

Engineering

Mathematics

Section Formulae and Centres of a Triangle

Tangent of Parabola

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( $m_{1}^{2} + m_{2}^{2}$ ) is equal to____.