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x+y=7 and a x^2+2h x y+a y^2=0,(a!=0) , ...

`x+y=7` and `a x^2+2h x y+a y^2=0,(a!=0)` , are three real distinct lines forming a triangle. Then the triangle is isosceles (b) scalene equilateral (d) right angled

A

isosceles

B

scalene

C

equilateral

D

right - angled

Text Solution

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The correct Answer is:
1
`ax^(2)+2hxy+ay^(2)=0`. Is symmetrical about `y=x`.
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CENGAGE-PAIR OF STRAIGHT LINES-Exercise (Single)
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  2. The straight lines represented by (y-mx)^(2)=a^(2)(1+m^(2))and(y-nx)^(...

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  3. If the pairs of lines x^(2)+2xy+ay^(2)=0andax^(2)+2xy+y^(2)=0 have e...

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  4. The condition that one of the straight lines given by the equation a...

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  5. If the represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated ...

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  6. The equations of a line which is parallel to the line common to the p...

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  7. The equation x^(2)y^(2)-9y^(2)+6x^(2)y+54y=0 represents

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  8. The equation a^2x^2+2h(a+b)x y+b^2y^2=0 and a x^2+2h x y+b y^2=0 repre...

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  9. If the equation of the pair of straight lines passing through the poin...

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  10. If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=- bisector of ...

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  11. Through a point A on the x-axis, a straight line is drawn parallel to ...

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  12. The image of the pair of lines represented by ax^(2)+2hxy+by^(2)=0by t...

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  13. The straight lines represented by the equation 135 x^2-136 x y+33 y^2=...

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  14. If the slope of one of the lines represented by ax^(2)+2hxy+by^(2)=0 ...

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  15. x+y=7 and a x^2+2h x y+a y^2=0,(a!=0) , are three real distinct lines ...

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  16. Statement 1 : If -h2=a+b , then one line of the pair of lines a x^2...

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  17. The orthocenter of the triangle formed by the lines xy=0 and x+y=1 is

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  18. Let PQR be a right - angled isosceles triangle , right angled at P(2,1...

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  19. Area of the triangle formed by the line x+y=3 and the angle bisectors ...

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  20. The orthocentre of the triangle formed by the lines 2x^(2)+3xy-2y^(2)...

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