Q) The minimum distance between the circle x squared space plus space y squared space equals space 9 space & space t h e space c u r v e space 2 x squared space plus 10 y squared space plus 6 x y equals 1 space i s space
left parenthesis A right parenthesis 2 square root of 2 space space space left parenthesis B right parenthesis 2 space space space space left parenthesis C right parenthesis 3 minus square root of 2 space space left parenthesis D right parenthesis square root of 2

Asked by araima2001 | 31st Mar, 2017, 05:17: AM

Expert Answer:

begin mathsize 16px style Given space circle space is space straight x squared plus straight y squared equals 9 space whose space centre space is space at space left parenthesis 0 comma 0 right parenthesis space and space radius space is space 3.
also comma space 2 straight x squared plus 10 straight y squared plus 6 xy equals 1
it space is space the space ellipse space whose space centre space is space at space origin.
solving space ax squared plus 2 hxy plus by squared plus straight c equals 0
using space angle space between space the space lines
tan 2 straight theta equals fraction numerator 2 straight h over denominator straight a minus straight b end fraction equals fraction numerator negative 3 over denominator 4 end fraction
fraction numerator 2 tan 2 straight theta over denominator 1 minus tan squared straight theta end fraction equals fraction numerator negative 3 over denominator 4 end fraction
you space will space get space tan straight theta subscript 1 equals 3 comma space space tanθ subscript 2 equals fraction numerator negative 1 over denominator 3 end fraction
these space lines space are space perpendicular space means space these space should space be space semi minus axes.
straight x equals rcosθ comma space straight y equals rsinθ
equation space of space ellipse space putting space these space values space in space the space given space ellipse space equation comma
and space solving
straight r equals 1 space and space fraction numerator 1 over denominator square root of 11 end fraction
the space semi minus major space axes space is space 1. space As space such space the space minimum space distance space between
space the space circle space and space the space ellipse space equals space 3 space minus space 1 space equals 2.
open parentheses Note colon space You space can space solve space these space equations space using space completing space square space method space also space you space will space get
equation space of space ellipse space as space straight x squared plus 11 straight y squared equals 1. close parentheses

end style

Answered by Sneha shidid | 31st Mar, 2017, 04:38: PM