QJEEM21Mad8ec: JEE Main 2021 Mathematics - Class 11 JEEM21Mad8ec Solution: Let a point P be such that its distance from the point (5, 0)…

Question

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Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (

-

5, 0). If the locus of the point P is a circle of radius r, then 4r² is equal to ________

Accepted Answer

Let P(h, k)

Given

PA = 3PB

PA² = 9PB²

\Rightarrow

(h

-

5)² + k² = 9[(h + 5)² + k²]

\Rightarrow

8h² + 8k² + 100h + 200 = 0

\therefore

Locus

{x^2} + {y^2} + \left( {{{25} \over 2}} \right)x + 25 = 0

\therefore

c \equiv \left( {{{ - 25} \over 4},0} \right)

\therefore

{r^2} = {\left( {{{ - 25} \over 4}} \right)^2} - 25

= {{625} \over {16}} - 25

= {{225} \over {16}}

\therefore

4{r^2} = 4 \times {{225} \over {16}} = {{225} \over 4} = 56.25

After Round of 4r² = 56

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