A geometry problem by Akhil Bansal
Two straight lines are perpendicular to each other, one of them touches the parabola =4a(x+a) and the other touches =4b(x+a) . Their point of intersection lies on the line
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1 solution
The second parabola is y^2=4b(x+b). Let y= m(x+a)+ a/m be the equation of the tangent to the first parabola and y = (-1/m)(x+b)-bm is the equation of the perpendicular tangent to the second parabola. On subtracting the equations,we get x+a+b=0.