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Q.

A line of fixed length a + b moves so that its ends are always on two fixed perpendicular straight lines. Then the locus of a point which divides this line into portions of length a and b is

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a

an ellipse 
 

b

a parabola 
 

c

a straight line 
 

d

a hyperbola 
 

answer is A.

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Detailed Solution

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AB=a+b⇒AB2=(a+b)2  α2+β2=(a+b)2 →(1) P(x, y)=bαa+b,aβa+b α=(a+b)xb  , β=(a+b)ya From (1)  (a+b)2x2b2+(a+b)2y2a2=(a+b)2  ⇒x2b2+y2a2=1 

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