"The locus of mid-points of the line segments joining ($-$3, $-$5) and the points on the ellipse ${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$ is :"

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"General point on ${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$ is A(2cos$\theta$, 3sin$\theta$)

given B($-$3, $-$5)

midpoint $C\left( {{{2\cos \theta - 3} \over 2},{{3\sin \theta - 5} \over 2}} \right)$

$h = {{2\cos \theta - 3} \over 2};k = {{3\sin \theta - 5} \over 2}$

$$ \Rightarrow {\left( {{{2h + 3} \over 2}} \right)^2} + {\left( {{{2k + 5} \over 3}} \right)^2} = 1$$

$\Rightarrow 36{x^2} + 16{y^2} + 108x + 80y + 145 = 0$"

The locus of mid-points of the line segments joining ($-$3, $-$5) and the points on the ellipse ${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$ is :

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The locus of mid-points of the line segments joining ($-$3, $-$5) and the points on the ellipse ${{{x^2}} \over 4} + {{{y^2}} \over 9} = 1$ is :

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