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Prove that the family of lines represent...

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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Given equation of lines is
`x(1+lambda)+y(2−lambda)+5=0`
`x+lambdax+2y−2ylambda+5=0`
`(x+2y+5)+lambda(x−y)=0`
...
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RD SHARMA ENGLISH-THE STRAIGHT LINES -All Questions
  1. Find the equation of the line passing through the point of intersectio...

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  2. Find the equation of the straight line drawn through the point of in...

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

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  4. Find the equation of the straight line passing through the point of in...

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  5. Find the equation of the line through the point of intersection of, th...

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  6. Write an equation representing a pair of lines through the point (a , ...

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  7. Write the coordinates of the orthocentre of the triangle formed by the...

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  8. If the centroid of a triangle formed by the points (0,0), (costheta, s...

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  9. Write the value of theta in (0,\ pi/2) for which area of the triangle ...

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  10. The distance between the lines 4x + 3y = 11 and 8x + 6y = 15 is

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  11. Write the coordinates of the orthocentre of the triangle formed by the...

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  12. If the lines x+a y+a=0,\ b x+y+b=0\ a n d\ c x+c y+1=0 are concurrent,...

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  13. Write the area of the triangle formed by the coordinate axes and the ...

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  14. Write the coordinates of the image of the point (3,8) in the lines x+3...

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  15. Write the integral values of m for which the x-coordinates of the poin...

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  16. The equation (b-c)x+(c-a)y+(a-b)=0 and (b^3-c^3)x+(c^3-a^3)y+a^3-b^3=0...

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  17. If a , b , c are in G.P. write the area of the triangle formed by the ...

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  18. Write the locus of a point the sum of whose distances from the coor...

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

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  20. Find the locus of the mid points of the portion of the lines xsintheta...

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