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If the lines ax+y+1=0, x+by+1=0, x+y+c=0...

If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and not equal to 1), are concurrent, then find the value of `1/(1-a)+1/(1-b)+1/(1-c)`

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PATHFINDER-CARTESIAN COORDINATES AND STRAIGHT LINE-QUESTION BANK
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  2. Find alpha if (alpha, alpha^2) lies inside the triangle having sides a...

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  3. If the lines ax+y+1=0, x+by+1=0, x+y+c=0, (a, b, c are distinct and no...

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  4. Prove that all lines represented by the equation (2costheta+3sintheta)...

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  5. A line through A(-5,-4) meets the lines x+3y+2=0, 2x+y+4=0 and x-y-5=0...

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  6. Given n straight line and a fixed point O, a straight line is drawn th...

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  7. Find the condition that two of the three lines represented by ax^3+bx^...

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  8. If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of para...

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  9. If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 represents a pa...

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  10. prove that the product of the perpendiculars drawn from the point (x1,...

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  11. The orthocentre of a triangle whose vertices are (0,0),(sqrt3,0) and (...

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  12. The image of the point (3,8) with respect to the line x+3y=7 is

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  13. The equations of the lines representing the sides of a triangle are 3x...

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  14. The point (4,1) undergoes the following three transformations successi...

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  15. A is (a,0) and B is (-a,0). If P is a point such that anglePAB - angle...

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  16. The points (-a,-b).(0,0),(a,b) and (a^2, ab) are

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  17. The medians AD and BE of a triangle ABC with vertices A(0, b), B(0, 0)...

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  18. The vertices of a rhombus taken in order are (2,-1), (3,4), (-2,3), th...

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  19. The coordinates of the point P on the lines 2x+3y+1=0, such that |PA-P...

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  20. One vertex of the equilateral triangle with centroid at the origin and...

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