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If the lines `a x+y+1=0,x+b y+1=0,` and `x+y+c=0(a , b , c` being distinct and different from 1) are concurrent, then `(1/(1-a))+(1/(1-b))+(1/(1-c))` is (a) 0 (b) 1 `1/((a+b+c))` (d) none of these

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If the lines a x+y+1=0,x+b y+1=0 and x+y+c=0(a ,b ,c being distinct and different from 1) are concurrent, then prove that 1/(1-a)+1/(1-b)+1/(1-c)=1.

If the lines a x+y+1=0,x+b y+1=0 and x+y+c=0(a ,b ,c being distinct and different from 1) are concurrent, then prove that 1/(1-a)+1/(1-b)+1/(1-c)=1.

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If the lines ax+y+1=0, x+by+1=0 and x+y+c=0 (a,b and c being distinct and different from 1) are concurrent the value of (a)/(a-1)+(b)/(b-1)+(c)/(c-1) is

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a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y+z=0, and x+y+c z=0 have nontrivial solution, then the value of 1/(1-a)+1/(1-b)+(1)/(1-c) is equal to a. 1 b. -1 c. z e ro d. none of these

If the lines a x+y+1=0,x+b y+1=0 and x+y+c=0 are concurrent (a!=b!=c!=1) , prove that 1/(1-a)+1/(1-b)+1/(1-c)=1 .

CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. The line parallel to the x-axis and passing through the intersection o...

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  2. The line L1:""y""-""x""=""0 and L2:""2x""+""y""=""0 intersect the line...

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

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  4. Two sides of a rhombus ABCD are parallel to the lines y = x + 2 and y ...

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  5. Equation(s) of the straight line(s), inclined at 30^(@) to the x-axis ...

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  6. If a pair of perpendicular straight lines drawn through the origin ...

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  7. The sides of a rhombus are parallel to the lines x+y-1=0 and 7x-y-5=0....

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  8. The image of P(a ,b) on the line y=-x is Q and the image of Q on t...

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  9. Consider a DeltaABC whose sides AB, BC and CA are represented by the s...

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  10. The equations of two equal sides A Ba n dA C of an isosceles triangle ...

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  11. Find the area of the triangle formed by the line x+y=3 and the angle b...

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  12. The sides of a triangle have the combined equation x^2-3y^2-2x y+8y-4=...

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  13. The equation of the lines passing through the point (1,0) and at a dis...

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  14. The number of values of k for which the lines (k+1)x+8y=4k and kx+(k+3...

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  15. For all real values of aa n db , lines (2a+b)x+(a+3b)y+(b-3a)=0 and m ...

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  16. The line x=c cuts the triangle with corners (0,0),(1,1) and (9,1) into...

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  17. The absolute value of the sum of the abscissas of all the points on th...

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  18. The point (x , y) lies on the line 2x+3y=6. The smallest value of the ...

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  19. The equations of the perpendicular bisectors of the sides A Ba n dA C ...

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  20. One of the diagonals of a square is the portion of the line x/2+y/3=2 ...

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