Two straight lines rotate about two fixed points $$(-a$$, $$O)$$ and (a$$,$$0) in anti clockwise direction. If they start from their position of coincidence such that one rotates at a rate double of the other, then locus of curve is

Question

Infinity Learn · Accepted Answer

Let PB make angle θ and PA make angle $$2$$θ with x $$-axis$$.  Let P is (h$$,$$k) . slope $$tan$$⁡θ$$=kh+a-----(1)$$$$tan$$⁡$$2$$θ$$=kh$$−$$a----(2)From$$ (2) $$2tan$$⁡θ$$1$$−$$tan2$$⁡θ$$=kh$$−aLocus on solving is $$2k(h+a)(h+a)2-k2=kh-a$$ $$2k(h2-a2)=k(h+a)2-k3h2+k2$$−$$2ah$$−$$3a2=0x2+y2$$−$$2ax$$−$$3a2=0$$

Two straight lines rotate about two fixed points (-a, O) and (a,0) in anti clockwise direction. If they start from their position of coincidence such that one rotates at a rate double of the other, then locus of curve is

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