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a1x+b1y+c1=0" and "a2x+b@y+c2=0 are……..e...

`a_1x+b_1y+c_1=0" and "a_2x+b_@y+c_2=0` are……..equations.

A

Parallel

B

Pair of linear

C

consistent

D

none

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The pair of equations a_1x+b_1y+c_1=0" and "a_2x+b_2y+c_2=0 has unique solution, then……..

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Show that two lines a_(1)x + b_(1) y+ c_(1) = 0 " and " a_(2)x + b_(2) y + c_(2) = 0 " where " b_(1) , b_(2) ne 0 are : (i) Parallel if a_(1)/b_(1) = a_(2)/b_(2) , and (ii) Perpendicular if a_(1) a_(2) + b_(1) b_(2) = 0 .

Theorem : A necessary and sufficient condition for the quadratic equations a_(1)x^(2)+b_(1)x+c_(1)=0" and "a_(2)x^(2)+b_(2)x+c_(2)=0 to have a common roots is (c_(1)a_(2)-c_(2)a_(1))^(2)=(a_(1)b_(2)-a_(2)b_(1))(b_(1)c_(2)-b_(2)c_(1))

The Cartesian equation of the sides BC,CA, AB of a triangle are respectively u_(1)=a_(1)x+b_(1)y+c_(1)=0, u_(2)=a_(2)x+b_(2)y+c_(2)=0 and u_(3)=a_(3)x+b_(3)y+c_(3)=0 . Show that the equation of the straight line through A bisectig the side bar(BC) is (u_(3))/(a_(3)b_(1)-a_(1)b_(3))=(u_(2))/(a_(1)b_(2)-a_(2)b_(1))

A : The area of the parallelogram formed by 4x-7y-13=0, 8x-y-39=0, 4x-7y+39=0, 8x-y+13=0 is 52. R : The area of the parallelogram formed by a_(1)x+b_(1)y+c_(1)=0, a_(1)x+b_(1)y+d_(1)=0, a_(2)x+b_(2)y+c_(2)=0, a_(2)x+b_(2)y+d_(2)=0 is |((c_(1)-d_(1))(c_(2)-d_(2)))/(a_(1)b_(2)-a_(2)b_(1))|

If two circles x^(2)+y^(2)+2a_(1)x+2b_(1)y=0 and x^(2)+y^(2)+2a_(2)x+2b_(2)y=0 touches then show that a_(1)b_(2)=a_(2)b_(1)

Assertion (A) : The normals to the planes x-lambday+z=1, 3x+2y-lambdaz+1=0 are perpendicular to each other if lambda+1=0 . Reason (R ) : If the planes a_(1)x+b_(1)y+c_(1)z+d_(1)=0,a_(2)x+b_(2)y+c_(2)z+d_(2)=0 are perpendicular to each other then a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2)=0

VGS PUBLICATION-BRILLIANT-PAIR OF LINEAR EQUATIONS IN TWO VARIABLES-EXERCISE
  1. The number of solutions to the pair of equations 11x-7y=6 and 4x+9y=8 ...

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  2. If the pair of equations kx+14y+8=0 and 3x+7y+6=0 has a unique solutio...

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  3. a1x+b1y+c1=0" and "a2x+b@y+c2=0 are……..equations.

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  4. If (a1)/(a2)=(b1)/(b2)=(c1)/(c2) then the lines will have………solutions.

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  5. 3x-2y+6=0,6x-4y+8=0 represents……….lines.

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  6. 5x-2y-10=0,10x-4y-20=0 these are………lines.

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  7. The number of solutions to 4x+6y-7=0 and 8x+5y-8=0 is………

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  8. (2)/(x)+(3)/(y)=2,(12)/(x)-(9)/(y)=3 then x=………

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  9. (2)/(x)+(3)/(y)=2,(12)/(x)-(9)/(y)=3 In the above problem y= …….

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  10. The lines x=5y passes through…………

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  11. Solve the following equations: 2^x+3^y=17" and "2^(x+2)-3^(y+1)=5

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  12. Solve the following equations: 2^x+3^y=17" and "2^(x+2)-3^(y+1)=5 In t...

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  13. Solve the following equations: (ax)/(b)-(by)/(a)=a+b, ax-by=2ab.

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  14. Solve the following equations: (ax)/(b)-(by)/(a)=a+b, ax-by=2ab. In th...

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  15. Slope of the line ax+by+c=0 is…………

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  16. The line ax+by+c=0 does not passes through………..

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  17. If x+y=7,x-y=1 then 2x =………..

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  18. In the above problem a5=…

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  19. Slope of the line y=x is………….

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  20. The line x=2015 is…….

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