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Show that the area of the triangle formed by the lines `y = m_(1) x + c_(1) , y = m_(2) x + c_(2) " and " x = 0 " is " ((c_(1) - c_(2))^(2))/(2|m_(1) - m_(2)|)`

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`((c_(2) - c_(1))^(2))/(2|m_(1) - m_(2)|)`
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If m_(1),m_(2) be the roots of the equation x^(2)+(sqrt(3)+2)x+sqrt(3)-1 =0 , then the area of the triangle formed by the lines y = m_(1)x,y = m_(2)x and y = 2 is

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Show that the equation of the straight line throught (alpha,beta) and through the point of intersection of the lines a_(1)x+b_(1)y+c_(1)=0 anda_(2)x+b_(2)y+c_(2)=0 is (a_(1)x+b_(1)y+c_(1))/(a_(1)alpha+b_(1)beta+c_(1))=(a_(2)x+b_(2)y+c_(2))/(a_(2)alpha+b_(2)beta+c_(2))

If m_1 and m_2 are the roots of the equation x^2-a x-a-1=0 , then the area of the triangle formed by the three straight lines y=m_1x ,y=m_2x , and y=a(a!=-1) is

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NCERT BANGLISH-STRAIGHT LINES-Miscellaneous Exercise on Chapter 10
  1. Show that the area of the triangle formed by the lines y = m(1) x + c(...

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  2. Find the values of k for which the line (k - 3) x - (4 - k^(2)) y +k^(...

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  3. Find the values of and p, if the equation x cos thita+ y sin theta = p...

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  4. Find the equations of the lines, which cut-off intercepts on the axes ...

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  5. What are the points on the y-axis whose distance from the linex/3 + y/...

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  6. Find perpendicular distance from the origin to the line joining the po...

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  7. Find the equation of the line parallel to y-axis and drawn through the...

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  8. Find the equation of a line drawn perpendicular to the line x/4 + y/6 ...

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  9. Find the area of the triangle formed by the lines y - x = 0, x + y = 0...

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  10. Find the value of p so that the three lines3x + y - 2 = 0, px + 2y - 3...

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  11. If three lines whose equations are y = m(1) x + c(1) , y = m(2) x + c(...

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  12. Find the equation of the lines through the point (3, 2) which make an ...

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  13. Find the equation of the line passing through the point of intersectio...

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  14. Show that the equation of the line passing through the origin and maki...

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  15. In what ratio, the line joining (-1, 1) " and " (5, 7) is divided by ...

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  16. Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) a...

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  17. Find the direction in which a straight line must be drawn through the ...

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  18. The hypotenuse of a right angled triangle has its ends at the points (...

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  19. Find the image of the point (3,8) with respect to the line x + 3y = 7 ...

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  20. If the lines y = 3x + 1 " and " 2y = x + 3 are equally inclined to the...

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

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