Conic Sections: Challenge #7
Sub-unit: Parabola
Let the parabola touches the line at a point P. If a line through P parallel to x-axis is drawn to meet at Q and R and the area of triangle OQR (where O is the origin) is A square units, then is equal to
The answer is 8.
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1 solution
Se x+y = 2 tangencia a parabola y=ax^2+3x+2, então a = 9/4.
Portanto, P = (-2/3, 8/3).
Daí, R, S são a intercessão de y = 8/3 e y+1 = |x|, ou seja, (+-11/3, 8/3).
Portanto, a área A = 2.1/2.(11/3)(8/3) = 88/9.
Assim, 9A/11 = 8.