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The equation ax^2+by^2+cx+cy=0 represent...

The equation `ax^2+by^2+cx+cy=0` represent a pair of straight lines , if

A

`a+b=0`

B

`a+c=0`

C

`b+c=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Te given equation will represent a pair of straight lines, if
`|(A,0,c//2),(0,b,c//2),(c//2,cR2,0)|=0`
`rArr" "-(ac^(2))/(4)-(bc^(2))/(4)=0rArr(c^(2))/(4)(a+b)=0rArra+b" "[becausecne0]`
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OBJECTIVE RD SHARMA ENGLISH-PAIR OF STRAIGHT LINES-Section I - Solved Mcqs
  1. The equation ax^2+by^2+cx+cy=0 represent a pair of straight lines , if

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  2. The equation 3x^2+2hxy+3y^2=0 represents a pair of straight lines pass...

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  3. If the pairs of straight lines ax^2+2hxy-ay^2=0 and bx^2+2gxy-by^2=0 b...

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  4. If ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents parallel straight lines, ...

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  5. If the equation 12x^(2)+7xy-py^(2)-18x+qy+6=0 represents a pair of pe...

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  6. The equation 8x^2 +8xy +2y^2+26x +13y+15=0 represents a pair of straig...

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  7. Let P Q R be a right-angled isosceles triangle, right angled at P(2,1)...

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  8. If the gradient of one of the lines x^(2)+hxy+2y^(2)=0 twice that of ...

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  9. The set of value of h for which the equation 4x^(2)+hxy-3y^(2)=0 repre...

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  10. If one of the lines of m y^2+(1-m^2)x y-m x^2=0 is a bisector of the a...

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  11. If one of the lines of the pair a x^2+2h x y+b y^2=0 bisects the angle...

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  12. The equation kx^2+4xy+5y^2=0 represents two lines inclined at an angle...

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  13. If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two ...

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  14. If the gradient one of the lines ax^2+2h x y+by^2=0 is twice that of t...

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  15. The equation x^(3)+y^(3)=0 represents

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  16. One bisector of the angle between the lines given by a(x-1)^(2)+2h(x-1...

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  17. The equation 2x^(2)-3xy-py^(2)+x+qy-1=0 represent two mutually perpend...

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  18. The product of the perpendiculars drawn from the point (1,2) to the pa...

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  19. The three lines whose combined equation is y^(3)-4x^(2)y=0 form a tria...

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  20. The angle between the pair of lines whose equation is 4x^(2)+10xy+my^...

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