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Prove that the family of lines represented by `x(1+lambda)+y(2-lambda)+5=0,lambda` being arbitrary, pass through a fixed point. Also find the fixed point.

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The correct Answer is:
`((-5)/3,(-5)/3)`
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ARIHANT MATHS ENGLISH-THE STRAIGHT LINES-Exercise For Session 3
  1. Locus of the point of intersection of lines x cosalpha + y sin alpha =...

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  2. If a ,\ b , c are in A.P., then the line a x+b y+c=0 passes through a ...

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  3. If the lines a x+12 y+1=0,\ b x+13 y+1=0 and c x+14 y+1=0 are concurre...

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  4. The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at th...

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  5. If the lines ax+y+1=0, x+by+1=0 and x+y+c=0 (a,b and c being distinct ...

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  6. If u=a1x+b1y+c1=0,v=a2x+b2y+c2=0, and (a1)/(a2)=(b1)/(b2)=(c1)/(c2), t...

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  7. The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent...

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  8. If the straight lines x+y-2=0,2x-y+1=0 and a x+b y-c=0 are concurrent,...

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  9. If the equations of three sides of a triangle are x+y=1, 3x + 5y = 2 a...

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  10. Find the equations of the line through the intersection of 2x - 3y + 4...

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  11. The locus of point of intersection of the lines x/a-y/b=m and x/a+y/b...

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  12. The condition on aa n db , such that the portion of the line a x+b y-1...

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  13. If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 a...

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  14. Prove that the lines ax+by + c = 0, bx+ cy + a = 0 and cx+ay+b=0 are ...

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  15. Find the equation of the straight line which passes through the inte...

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  16. Let a ,\ b ,\ c be parameters. Then the equation a x+b y+c=0 will repr...

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  17. Prove that the family of lines represented by x(1+lambda)+y(2-lambda)+...

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  18. Prove that (-a,-a/2) is the orthocentre of the triangle formed by the ...

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