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If the coordinates of avariable point P be (acostheta,bsintheta) whre theta is variable quantity , find the locus of P.

If the coordinates of avariable point P be (acostheta,bsintheta) whre theta is variable quantity , find the locus of P.
 

Grade:11

3 Answers

Nicho priyatham
625 Points
5 years ago
by eleminating teta we get
(x/a)2+(y/b)2=1
which is an ELLIPSE
plz approve if useful
Shravani
13 Points
3 years ago
P(x,y)=p(a cos theta,b sin theta ) X=a cos theta y= b sin theta X/a = cos theta y/b sin theta Squaring on both sides X^2/a^2= cos ^2theta y^2/b^2=sin^2theta Adding both X^2/a^2 +y^2/b^2 =1Hence proved
Anmol jain
11 Points
3 years ago
X=acostheta ; Y=bsinthetaX/a=cos there; Y/b=bsinthetaSquaring both the equationsX^2 /a^2=cos^2theta;y^2/b^2=sin^2 thetaAdding both equationsX^2b^2+y^2a^2=a^2b^2. (Cos^2theta +sin^2theta=1)

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