What is the equation of directrix of parabola y^{2}=4bx where b \lt 0 and b^{2}+b-2=0?

Explanation

Solving the quadratic equation b^2+b-2=0 yields (b+2)(b-1)=0, so b=-2 or b=1. Since b \lt 0, we have b=-2. The parabola equation becomes y^2 = -8x. Comparing this with standard form y^2 = 4Ax, we get A = -2. The directrix of the parabola is x = -A, which means x = 2, or x-2=0.

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