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 ⇒(y−y1x−x1)(y−y2x−x2)=−1 ⇒(x−x1)(x−x2)+(y−y1)(y−y2)=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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