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Show that for all values of a,b and c the line `(b-c)x+(c-a)y+a-b=0` always passes through the point (2,3).

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The correct Answer is:
`tan^(-1)((a)/(2b+a))`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. Prove that diagonals of the parallelogram formed by the four straight ...

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  2. Find the locus of the foot of the perpendicular from the origin upon ...

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  3. Show that for all values of a,b and c the line (b-c)x+(c-a)y+a-b=0 alw...

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  4. Show that the locus of the point of intersection of the stright lines ...

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  5. Prove analytically that in any triangle the perpendiculars drawn from ...

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  6. Prove analytically that the bisectors of the interior angles of a tria...

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  7. If d(1),d(2),d(3) be the distances of a fixed point from the straight ...

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  8. Show that the quadrilateral formed by the four lines y=mx+a sqrt(a+m^(...

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  9. Show that the lines x cos alpha+ y alpha=p, x cos (alpha+ (2pi)/(3)) +...

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  10. 2x-y+4=0 is a diameter of a circle which circumscribes a rectangle ABC...

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  11. ABC is right-angle triangle, right -angled at A. The coordinates of B ...

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  12. The line through A( a cos theta,0) and perpendicular to the x-axis mee...

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  13. P and Q are two point on the line x-y+1=0, if O is the origin and bar...

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  14. O(0,0) and A(4,4) are two given points and B is any point. Find the eq...

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  15. Show that the image of the point (h,k) with respect to the striaight l...

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  16. A point moves so that sum of the squares of its distances from the ve...

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  17. Find the locus of mid points of chords of the cirlce. x^(2)+y^(2)=a^(2...

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  18. A straight line is such that its segment between lines 5x-y-4=0 and 3x...

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  19. A rod of length a unit slides on the x-axis and another rod of length ...

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  20. A circle cuts intercepts of length 2a unit and 2b unit from the x-axis...

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