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If p and q are respectively the perpendi...

If p and q are respectively the perpendiculars from the origin upon the striaght lines, whose equations are ` x sec theta + y cosec theta =a and x cos theta -y sin theta = a cos 2 theta , then 4p^(2) + q^(2)` is equal to

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(cosec theta -sin theta ) (sec theta - cos theta ) (tan theta + cot theta ) = 1.

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If p and q are the lengths of perpendiculars from the origin to the lines xcos theta -ysin theta = k cos 2 theta and x sec theta + y cosec theta= k , respectively, prove that p^2 + 4q^2 = k^2 .

Prove that : (sin theta)/(1+cos theta) + (1+cos theta)/(sin theta)= 2 cosec theta .

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MODERN PUBLICATION-STRAIGHT LINES -EXERCISE
  1. Find perpendicular distance of the line joining the points (cos theta,...

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  2. If p is the length of perpendicular from the origin to the line whose ...

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  3. If p and q are respectively the perpendiculars from the origin upon th...

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  4. If p and q are the lengths of perpendicular from origin to the lines x...

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  5. Find the length of the perpendicular from the vertex B of triangle ABC...

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  6. Find the distance between the parallel lines : 4x - 3y -9 =0 and 4x ...

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  7. Find the distance between the parallel lines (i) 15x+8y-34=0 and 15x...

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  8. Find the distance between the parallel lines : l(x + y) + p =0 and l...

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  9. The perpendicluar distance of a st. line from the origin is 5cm and it...

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  10. If sum of the perpendicular distances of a variable point P (x, y) fro...

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  11. Find the equation of the line which is equidistant from parallel lines...

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  12. Prove that the product of the lengths of the per-pendiculars drawn fro...

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  13. If 5x- 12y+26=0 and 5x- 12y- 65 = 0 are the equations of a pair of opp...

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  14. Find the equations of the bisectors of the angles formed by the follow...

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  15. Find the equations of the bisectors of the angles formed by the follow...

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  16. Find the equations of the bisectors of the angles formed by the follow...

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  17. Find the equations of the bisectors of the angles formed by the follow...

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  18. Find the equations of the bisectors of the angles formed by the follow...

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  19. Prove that the bisectors of the angles formed by pairs of lines are pe...

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  20. Prove that the bisectors of the angles formed by pairs of lines are pe...

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