QJEEM21Ma298f: JEE Main 2021 Mathematics - Class 11 JEEM21Ma298f Solution: The locus of mid-points of the line segments joining ( 3, 5)…

Question

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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 :

Accepted Answer

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

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