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#1. The illumination at a point is inversely proportional to the square of the distance of the point from the light source and directly porportional to the intensity of the light source. If two light sources are z feet apart and their intensities are A and B respectively, at what point between them will the sum of their illuminations be at a minimum? Let x be the distance from A at which the sum of the illumination be minimum.
Give answer in terms of z, A, B.
#2. Find the equation of the line that is tangent to the ellipse b^2x^2+a^2y^2=a^2b^2 in the first quadrant and form with the coordinate axes the triangle with the smallest possible area.
a and b are positive constants
___x + ___y + ____= 0