    Question

# lf the line xcos α+ ysin α=p and the circle x2+y2=a2 intersect at A and B then the equation of the circle on AB as diameter (x2+y2−a2)+k(xcosα+ysinα−p)=0 then k=

A
p
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B
p
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C
4p
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D
2p
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Solution

## The correct option is B −2pCentre of the circle having AB as diameter is the foot of perpendicular from (0,0) to x cos α+y sin α=p thenx−0cos α=y−0sin α=−(−p)1x=p cos α and y=p sin αEquation of circle having centre (p cos α,p sin α) andradius(r)=√a2−(√p2(sin2α+cos2α))2=√a2−p2∴(x−p cos α)2+(y−p sinα)2=(√a2−p2)2x2+y2−a2+p2−x2p cos α−2py sin α+p2=0(x2+y2−a2)−2p(2cos α x+2sin α y−p)=0So, k=−2p∴AB=2r   Suggest Corrections  0      Similar questions  Related Videos   Parametric Representation-Ellipse
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