Tangents PA and PB are drawn to the circle x 2 +

Question

Tangents PA and PB are drawn to the circle x2 + y2 = 4, then the locus of the point P if the triangle PAB is equilatera

gangula deekshith · Accepted Answer

given circle x2+y2=4then the radius of the circle is r=2we know that the circle centre (g,f) lies on the origin (0,0)given that PAB is equilateral triangle so ang(A)=ang(B)=ang(P)=600let PD be the altittude of the triangle then ang(OPB)=ang(OPA)=300 according to pythagorus theorem consider triangleOPBhere OB=2 (OB is the raduis of the circle)cos300=BP/OA3½/2=BP/2BP=3½similarly AP=31/2AP+BP=2(31/2)we know that (x-h)2+(y-k)2=0 here (h,k)=(31/2,31/2)x2+2(31/2)x -8 +y2+2(31/2)y-8=0 x2+y2-16=0 [cirlce centre lies on the origin so (g,f)=0x2+y2=16

Analytical Geometry> Tangents PA and PB are drawn to the circl...

Tangents PA and PB are drawn to the circle x2 + y2 = 4, then the locus of the point P if the triangle PAB is equilatera

SMILE FREE FIRE , 3 Years ago

gangula deekshith

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Analytical Geometry> Tangents PA and PB are drawn to the circl...

Tangents PA and PB are drawn to the circle x2 + y2 = 4, then the locus of the point P if the triangle PAB is equilatera

SMILE FREE FIRE , 3 Years ago

gangula deekshith

LIVE ONLINE CLASSES

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