Home
Class 12
MATHS
Prove that the area of the parallelogram...

Prove that the area of the parallelogram contained by the lines `4y-3x-a=0,3y-4x+a=0,4y-3x-3a=0,` and `3y-4x+2a=0` is `(2/7)a^2dot`

Text Solution

Verified by Experts


` tan theta =|((4//3)-(3//4))/(1+(4//3) xx (3//4))| = (7)/(24)`
` or "cosec" theta = (25)/(7)`
` "Now " d_(1) = (|-a+3a|)/(5) = |(2a)/(5)`
`"and " d_(2) = (|2a-a|)/(5) = |(a)/(5)|`
`therefore " Area" = 2("Area of" Delta ABD") = 2 ((1)/(2)d_(1) * AB)`
` = d_(1)d_(2) "cosec " theta = (|(a)/(5)|)(|(2a)/(5)|)(25)/(7)= (2a^(2))/(7) `
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXAMPLE|12 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.1|23 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

Prove that the area of the parallelogram formed by the lines 3x-4y+a=0,\ 3x-4y+3a=0,\ 4x-3y-a=0\ a n d \4x-3y-2a =0\ i s (2a^2)/7s qdotu n i t sdot

The triangle formed by the lines x+y =0,3x+y=4 and x+3y=4 is-

The orthocentre of the triangle formed by the lines x+y=1,2x+3y=6 and 4x-y+4=0 lies in

Find the circumcentre and circumradius of the triangle formed by the lines 3y - 4x-1 = 0, y -x -3 = 0 and x +y -5 = 0 .

The orthocentre of the triangle formed by the lines 2x^(2)+3xy-2y^(2)-9x+7y-5=0 with 4x+5y-3=0 is

Find the angle between the lines x-3y-4=0,4y-z+5=0a n dx+3y-11=0,2y+z+6=0.

The triangle formed by the line x+sqrt3y=0, x- sqrt3y=0 and x=4 is-

Prove that the point (2,2) is equidistant from the three straight lines 4x+3y-4=0,12x-5y+12=0and3x-4y=8.

Column I|Column II a.Four lines x+3y-10=0,x+3y-20=0,3x-y+5=0,a n d3x-y-5=0 form a figure which is|p. a quadrilateral which is neither a parallelogram nor a trapezium b.The points A(1,2),B(2,3),C(-1,-5),a n dD(-2,4) in order are the vertices of|q. a parallelogram c.The lines 7x+3y-33=0,3x-7y+19=0,3x-7y-10 , and 7x+3y-4=0 form a figure which is|r. a rectangle of area 10 sq. units d.Four lines 4y-3x-7=0,3y-4x+7=0,4y-3x-21=0,3y-4x+14=0 form a figure which is|s. a square

Find the area cut off from the parabola 4y =3x^(2) by the straight line 3x-2y +12=0