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Find the equation of the diagonals of th...

Find the equation of the diagonals of the parallelogram formed by the lines `ax+by`

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The correct Answer is:
`(a+a')x+(b+b') y+c+c'=0 and (a-a')x+(b-b')y=0 and a^(2)+b^(2)=a^('2)+b^('2)`
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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. A is a point on the circle x^(2)+y^(2)=36. Find the locus of the point...

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  2. The coordinates of the points A and B are (1,3) and (-2,1) respectivel...

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  3. Find the equation of the diagonals of the parallelogram formed by the ...

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  4. Show that the lines y=0, sqrt(3y)-xy=sqrt(3) and sqrt(3y)+x-10=0 form ...

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  5. Prove analytically that the perpendicular bisector of the sides of a t...

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  6. The coordinates of the vertex A of the triangle ABC are (-5,2) the equ...

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  7. The coordinates of the vertices of a triangle are [at(1)t(2),a(t(1)+t(...

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  8. Prove that diagonals of the parallelogram formed by the four straight ...

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

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  10. 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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  11. Show that the locus of the point of intersection of the stright lines ...

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

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

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

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

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

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  17. 2x-y+4=0 is a diameter of a circle which circumscribes a rectangle ABC...

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

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

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

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