From a point P , the chord of contact to the ellipse E1 : x^2/3 + y^2/4 = 1 touches the ellipse E2: x^2/9 + y^2/16 = 1 , locus of P satisfy (a,5) then [ a ] = ?? (where [ ] denotes the greatest integer function) .
Answer is 4 .

Dear Student,
Please find below the solution to the asked query:

We havex23+y24=1For point h,k chord of contact to above ellipse is given byT=0xh3+yk4=14xh+3yk=123yk=-4xh+12y=-4h3kx+4kNow compare with y=mx+cm=-4h3k and c=4kNow y=mx+c is tangent to ellipse x2a2+y2b2=1if c2=a2m2+b2Hence  x29+y216=1 will have tangent as y=mx+c if  c2=9m2+1616k2=916h29k2+161k2=h2k2+11=h2+k2Hence locus is x2+y2=1Point a,5 cannot lie on this curve because right hand can only go upto 1.Please recheck your question  

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