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Question

Let A(x1,y1) and B(x2,y2) are two fixed points.Then locus of point P such that

A
APB=90o is a circle
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B
Area of APB is minimum is a parabola
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C
AP+PB=K where K<AB is an ellipse
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D
APPB=K where K<1 is a circle
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Solution

The correct options are
A APB=90o is a circle
D APPB=K where K<1 is a circle
(1) APB=90o(slope of AP)(slope of PB)=1

(yy1xx1)(yy2xx2)=1
(xx1)(xx2)+(yy1)(yy2)=0
which is a circle

(2) Area of APB is minimum
APB=0
A,P,B are collinear

(3) AP+PB=K;if k=AB:Straight line
k>AB:an ellipse
k<AB:no solution

(4) APPB=K If k=1

then locus is straight line and if k<1 or k>1 then locus is circle

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