st line

JEE Mains 2015 Online › Co-ordinate Geometry questions › st line

if the point [3,4] lies on the locus of the point of intersection of the lines xcos(Î±)+ysin(Î±)=a and xsin(Î±)-ycos(Î±)=b, (Î± is variable), the point (a,b) lies on the line 3x-4y=0 then 9a⁴+16b⁴+34 is equal to

#Mathematics #Co-ordinate Geometry #Straight line

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2 Answers

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Amartya Kumar Mistry ·2014-08-20 22:33:16

at first find locus of point of intersection of the two given lines
xcosÎ±+ysinÎ±=a...........(1)
xsinÎ±-ycosÎ±=b...................(2)
now squaring and adding eq 1 and 2 will give you locus as
x^2+y^2=a^2+b^2
now (3,4) will satisfy this eq
we get a^2+b^2=25
and also (a,b) lies on 3x-4y=0 from there you will get the relation between a and b then you will get the answer.