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Equations of two straight lines are xcos...

Equations of two straight lines are `xcos alpha + ysin alpha = p and xcos beta + ysin beta = p'.` Show that the area of the quadrilateral formed by the two lines and the perpendiculars drawn from the origin to the lines is `1/(2sin (B-alpha)) [2pp'-(p2 +p'2) cos(alpha-beta)}.`

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A DAS GUPTA-Coordinates and Straight Lines-EXERCISE
  1. The equations of the perpendicular bisectors of the sides A Ba n dA C ...

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  2. If (h, r) is the foot of the perpendicular from (x1, y1) to lx+my+n=0,...

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  3. Equations of two straight lines are xcos alpha + ysin alpha = p and xc...

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  4. The side AB,BC,CD and DA of a quadrilateral are x+2y=3, x=1, x-3y=4, 5...

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  5. Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E...

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  6. Show that the lines 4x+y-9=0,x-2y+3=0,5x-y-6=0 make equal intercepts o...

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  7. A line through the variable point A(k+1,2k) meets the lines 7x+y-16=0,...

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  8. A straight line through the point A(-2, -3) cuts the line x+3y=9 and x...

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

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  10. The sides A Ba n dA C of a triangle A B C are respectively 2x+3y=29a n...

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  11. Find the equations of the lines which pass through the point (4,5) and...

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  12. Find the bisector of acute angle between the lines x+y - 3 = 0 and 7x ...

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  13. Determine whether the origin lies inside or outside the triangle whose...

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  14. The equation of the bisector of the angle between the lines x+2y-2=0, ...

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  15. Find the values of beta so that the point (0,beta) lies on or inside t...

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  16. Given vertices A (1, 1),B(4, -2)&C(5, 5) of a triangle, find the equat...

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  17. Find the equation of the sides of a triangle ABC with A(1,3) as a vert...

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  18. Find the equation of the legs of a right isosceles triangle if the equ...

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  19. In a right angled triangle the vertex at the right angle is (1,1), one...

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  20. The ends of the base of an isosceles triangle are at (2a, 0)and (0, a)...

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