QJEEM19Maf800: JEE Main 2019 Mathematics - Class 11 JEEM19Maf800 Solution: Let O(0, 0) and A(0, 1) be two fixed points. Then the locus of…

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Let O(0, 0) and A(0, 1) be two fixed points. Then the locus of a point P such that the perimeter of

\Delta

AOP is 4, is :

Accepted Answer

Let point C(h, k)

Given, AB + BC + AC = 4

From graph, AB = 1

\therefore

BC + AC = 3

\Rightarrow

\sqrt {{h^2} + {k^2}} + \sqrt {{h^2} + {{\left( {k - 1} \right)}^2}} = 3

\Rightarrow

{{h^2} + {{\left( {k - 1} \right)}^2}}

= 9 +

{{h^2} + {k^2}}

-

6\sqrt {{h^2} + {k^2}}

\Rightarrow

6\sqrt {{h^2} + {k^2}} = 2k + 8

\Rightarrow

9\left( {{h^2} + {k^2}} \right) = {k^2} + 8k + 16

\Rightarrow

9{h^2} + 8{k^2} - 8k - 16 = 0

\therefore

Locus of point C will be,

9x² + 8y² – 8y = 16

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