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Q)Let bx + ay =ab and ax+by=1 be twovariable lines and a,b be parameters such that a2+b2=ab,then the locus of point of intersection of the lines isa)x2+y2+xy+1=0b)x2+y2-xy+1=0c)x2+y2+xy-1=0d)x2+y2-xy-1=0

Sibashis ghosh , 10 Years ago
Grade 11
anser 1 Answers
UPINDERJEET SINGH

Last Activity: 10 Years ago

Let (p,q) be their point of intersection.
therefore:
bp+aq=ab
& ap+bq=1
multiply both,
abp^2+b^2pq+a^2pq+abq^2=ab
ab(p^2+q^2) + pq(a^2+b^2)=ab
but given (a^2+b^2)=ab
so,
ab(p^2+q^2+pq)=ab
thus,
p^2+q^2+pq-1=0
therefore locus is: x^2+y^2+xy-1=0 ie. c)

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