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

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