If A(2,0) and B(0,2) are given points and P is a point such that PA:PB=2:3, then the locus of P passes through the point (a,a) for
A
a>2
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B
a=1
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C
no real value of a.
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D
finite number of real values of a.
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Solution
The correct option is C no real value of a. Let P(x,y) be such that PA:PB=2:3 then 9(PA)2=4(PB)2 ⇒9[(x−2)2+y2]=4[x2+(y−2)2] ⇒9(x2+y2−4x+4)=4(x2+y2−4y+4) ⇒5x2+5y2−36x+16y+20=0 which is the locus of P and it passes through (a,a) if 5a2+5a2−36a+16a+20=0 or 10a2−20a+20=0 or (a−1)2+1=0 which is not possible for any real value of a.