# Conic Sections: Challenge #7

Geometry Level 3

Sub-unit: Parabola

Let the parabola $y = ax^{2} + 2x + 3$ touches the line $x+ y -2 =0$ at a point P. If a line through P parallel to x-axis is drawn to meet $y + 1 = \mid x \mid$ at Q and R and the area of triangle OQR (where O is the origin) is A square units, then $\frac{9A}{11}$ is equal to

×