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Let P any point on ellipse 3x^(2)+4y^(2)...

Let P any point on ellipse `3x^(2)+4y^(2)=12` . If S and S'' are its foci then find the the locus of the centroid of trianle PSS''

Text Solution

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The correct Answer is:
`(9x^(2))/(4)+3y^(2)=1`
We have ellipse `(x^(2))/(4)+(y^(3))/(3)=1`
`a^(2)e^(2)=a^(2)-b^(2)=4-3=1`
Thus, foci are S(1,0) and S'(-1,0)
Variable point P on the ellipse is `(2 cos theta, sqrt(3) sin theta)`.
Let centrod of triangle PSS' be R(h,k)
`:. 3h=1-1+2 cos theta and 3 k=0+0+sqrt(3)sin theta`
`:. cos theta=(3h)/(2) and sin theta=(3)k`
Squaring and adding, we get
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