Q.

At the point of intersection of the rectangular hyperbolaxy=c2 and the parabola y2=4ax tangents to the  rectangular hyperbola and the parabola make angles θ and ϕ , respectively with x -axis, then

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Detailed Solution

Let x1,y1 be point of intersection. ⇒    y12=4ax1,x1y1=c2 For     y2=4axmTx1,y1=2ay1=tan⁡ϕ For xy=c2,MTx1,y1=−y1x1=tan⁡θ So      tan⁡θtan⁡ϕ=−y122ax1=−4ax12ax1=−2 So  θ=tan−1⁡(−2tan⁡ϕ)
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At the point of intersection of the rectangular hyperbolaxy=c2 and the parabola y2=4ax tangents to the  rectangular hyperbola and the parabola make angles θ and ϕ , respectively with x -axis, then