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The triangle formed by the lines whose c...

The triangle formed by the lines whose combined equation is `(y^2 - 4xy - x^2)(x + y - 1) = 0` is

A

equilateral

B

right angled

C

isosceles

D

obtuse angled

Text Solution

Verified by Experts

The correct Answer is:
B
The equation of the sides of the triangle are given by
`y^(2)-4xy-x^(2)=0 and x+y-1=0`
Clearly, `y^(2)-4xy-x^(2)=0` represents a pair of perpendicular lines.
Hence, the triangle is right angled.
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OBJECTIVE RD SHARMA ENGLISH-PAIR OF STRAIGHT LINES-Section I - Solved Mcqs
  1. The equation of two straight lines through the point (x(1),y(1)) and p...

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  2. The equation of the straigh lines through the point (x(1),y(1)) and pa...

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  3. The triangle formed by the lines whose combined equation is (y^2 - 4xy...

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  4. Find the combined equation of the pair of lines through the point (1, ...

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  5. The equation x^(3)+ax^(2)y+bxy^(2)+y^(3)=0 represents three straight l...

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  6. The combined equation of the lines L(1) and L(2) is 2x^(2)+6xy+y^(2)=0...

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  7. The lines represented by x^(2)+2lambda xy+2y^(2)=0 and the lines repre...

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  8. Prove that the equation m (x^3-3xy^2)+y^3-3x^2y=0 represents three str...

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  9. If the equation x^(4)+bx^(3)y+cx^(2)y^(2)+dxy^(3)+ey^(4)=0 represent t...

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  10. The equation x^(3)+x^(2)y-xy^(2)-y^(3)=0 represents three straight lin...

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  11. If one of the lines of my^(2)+(1-m^(2))xy-mx^(2)=0 is a bisector of th...

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  12. The equation x^2 - 3xy+ lambday^2 + 3x - 5y + 2 = 0 where lambda is a ...

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  13. If the line y = mx bisects the angle between the lines ax^2 + 2h xy ...

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  14. Two pairs of straight lines have the equations y^(2)+xy-12x^(2)=0andax...

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  15. The point of intersection of the pair of straight lines given by 6x^(2...

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  16. The straight lines represented by x^2+m x y-2y^2+3y-1=0 meet at (a) (-...

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  17. The square of the distance between the origin and the point of interse...

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  18. The centroid of the triangle whose three sides are given by the combin...

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  19. If first degree terms and constant term are to be removed from the equ...

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  20. The combined equation of three sides of a triangle is (x^2-y^2)(2x+3y-...

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