Find the vertices and foci of the conic section without axis rotation by analyzing the...

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2022-01-17

Find the vertices and foci of the conic section without axis rotation by analyzing the graph geometrically in the xy-plane. (Note dun all four graphs ore symmetric about the lines y=x and y=x.) The hyperbola xy=4

Answer & Explanation

nick1337

nick1337

Expert

2022-01-19Added 573 answers

Step 1 Since cot2θ=adjopp, we let adj=5 and opp=12. By the Pythegorean Theorem, (hyp)2=(adj)2+(opp)2 (hyp)2=52+122 (hyp)2=169 hyp=±13 Since 0<θ<π2, then 0<2θ<π. Since cot2θ>0 in QI, then cos2θ>0. So, we take hyp=13 cos2θ=adjhyp cos2θ=513

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