Home
Class 12
MATHS
Find the value of lambda if the equation...

Find the value of `lambda` if the equation `9x^2+4y^2+2lambdax y+4x-2y+3=0` represents a parabola.

Text Solution

Verified by Experts

Comparing the given equation with `ax^(2)+by^(2)+2hxy+agx+2fy+c=0`, we have `a=9,b=4,c=3,h=lamda,g=2,andf=-1`. If the equation `9x^(2)+4y^(2)+2lamdaxy+4x-2y+3=0` represents a parabola, then its second-degree terms must form the perfect square. Therefore,
`lamda^(2)=36" ""(Using "h^(2)-ab=0)`
`orlamda=pm6`
Also, for these values of `lamda,Delta!=0`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.26|2 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.27|1 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.24|1 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

Find the value of lambda if the equation (x-1)^2+(y-2)^2=lambda(x+y+3)^2 represents a parabola. Also, find its focus, the coordinates of its vertex, the equation of its latus rectum

Show that the equation 9x^2-16 y^2-18 x+32 y-151=0 represents a hyperbola.

Knowledge Check

  • The value of lambda so that the equation lambda x^2+2xy+lambday^2+4x+4y+3=0 represent a pair of straight lines is

    A
    `5/3`
    B
    `5/31`
    C
    1
    D
    none of these

  • The equation y^(2) + 4x + 4y + k = 0 represents a parabola whose latus rectum is _

    A
    1
    B
    2
    C
    3
    D
    4

    • Similar Questions

    Explore conceptually related problems

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

    The second degree equation x^2+4y^2-2x-4y+2=0 represents

    Examine whether the equation x^(2) + y^(2) - x - 4y + 7 = 0 represents a circle.

    The equation y^(2)+4x+4y+k=0 represents a parabola whose latus rectum is

    Does equation (5x-5)^(2)+(5y+10)^(2)=(3x+4y+5)^(2) represents a parabola ?

    Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

    Home
    Profile