AP EAMCET20226 Jul 2022Morning ShiftMathematicsStraight LinesActual

A point P(x, y) is such that its distance from (-1,0) and (0,2) are in a ratio of 2 : 1 . Then the locus of P is

Options

A(x-1)^2+(y-4)^2=10
B(x+2)^2+(y+2)^2=10
C(x-1)^2+(y-4)^2=100
D(x+2)^2+(y+2)^2=100

Correct answer

A. (x-1)^2+(y-4)^2=10

Step-by-step solution

Given P(x, y),(-1,0) and (0,2) Let A(-1,0) and B(0,2) aligned & PA P ( B ) = 2 1 Given & ( x +1)^2+( y -0)^2 ( x -0)^2+( y -2)^2 = 2 1 & x ^2+1+2 x + y ^2=2 x ^2+2 y ^2+8-8 y & x ^2+ y ^2-2 x -8 y +7=0 & ( x -1)^2+( y -4)^2=10 aligned

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