Prove that the point of intersection of two tangents to the hyperbola, the product of whose slopes is c2, lies on the curve y2 + b2 = c2(x2 – a2).

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Two parallel beams of light P and Q are incident normally on a prism and the transmitted rays are brought to focus with the help of a convergent lens as shown. If the intensities of the upper and lower beams immediately after transmission from face AC are 4I abd I, respectively, find the resultant intensity at the focus.

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The system of connected flexible cables shown in the figure is supporting 2 loads of 550N and 600N at points B and D. Determine the tensions in various segments of the cable