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

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NCERT BANGLISH-STRAIGHT LINES-EXERCISE 10.3
  1. Reduce the following equations into slope - intercept form and find th...

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  2. Reduce the following equations into intercept form and find their inte...

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  3. Reduce the following equations into normal form. Find their perpendicu...

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  4. Find the distance of the point (-1, 1) from the line 12 (x + 6) = 5 (...

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  5. Find the points on the x-axis, whose distances from the line x/3 + y/...

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

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  7. Find equation of the line parallel to the line 3x - 4y + 2 = 0 and pa...

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  8. Find equation of the line perpendicular to the line x - 7y + 5 = 0 an...

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  9. Find angles between the lines sqrt3x + y = 1 " and " x + sqrt3y = 1.

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  10. The line through the points (h, 3) and (4,1) intersects the line 7x -...

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  11. Prove that the line through the point (x(1) , y(1)) and parallel to th...

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  12. Two lines passing through the point (2, 3) intersects each other at an...

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  13. Find the equation of the right bisector of the line segment joining th...

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  14. Find the coordinates of the foot of perpendicular from the point (-1, ...

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  15. The perpendicular from the origin to the line y = mx + c meets it at t...

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  16. If p and q are the lengths of perpendiculars from the origin to the li...

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  17. In the triangle ABC with vertices A (2, 3) , B (4, -1) " and " C (1, ...

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

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