Home
Class 12
MATHS
Show that the equation a(x^4+y^4)-4bxy(x...

Show that the equation `a(x^4+y^4)-4bxy(x^2-y^2)+6cx^2y^2=0` represents two pairs of lines at right angles and that `if 2b^2=a^2+3ac` , the two pairs will coincide.

Text Solution

Verified by Experts

The correct Answer is:
` therefore 2b^2=a^2+3ac`
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 1|9 Videos
  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 2|10 Videos
  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos
  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

Similar Questions

Explore conceptually related problems

The equation 3x^2+2hxy+3y^2=0 represents a pair of straight lines passing through the origin . The two lines are

if lambda x^2+10xy+3y^2-15x-21y+18=0 represents a pair of straight lines. Then , the value of lambda is

The equation of second degree x^2+2sqrt2xy+2y^2+4x+4sqrt2y+1=0 represents a pair of straight lines.The distance between them is

Equation ax^3-9x^2y-xy^2+4y^3=0 represents three straight lines. If the two of the lines are perpendicular , then a is equal to a. -5 b. 5 c. -4 d. 4

For what value of lambda does the equation 12x^2-10xy+2y^2+11x-5y+lambda=0 represent a pair of straight lines ? Find their equations and the angle between them.

Show that the equation of the pair of lines bisecting the angles between the pair of bisectors of the angles between the pair of lines ax^(2)+2hxy+by^(2)=0 is (a-b)(x^(2)-y^(2))+4hxy=0

Solve the pair of equations: 2/x+3/y=13 5/x-4/y=-2

Show that the circles x^(2)+y^(2)-6x+4y+4=0and x^(2)+y^(2)+x+4y+1=0 cut orthogonally.

Show that the differential equation that represents the family of all parabolas having their axis of symmetry coincident with the axis of x is y y_2+y1 2=0.

Two rails are represented by the equations x+2y-4=0 and 2x+4y-12=0 Represent this situation geometrically.