Home
Class 12
MATHS
If the equation a x^2-6x y+y^2 +2gx +2fy...

If the equation `a x^2-6x y+y^2 +2gx +2fy +c=0` represents a pair of lines whose slopes are `m` and `m^2,` then the value(s) of `a` is/are

A

`a=-8`

B

`a=8`

C

`a=27`

D

`a=-27`

Text Solution

Verified by Experts

The correct Answer is:
2, 4
`m and m^(2)` are the roots of equation
`((y)/(x))^(2)-6((y)/(x))+a=0`
`:. m+m^(2)=6andm^(3)=a`
or `m^(3)+m^(6)+3m^(3)(m+m)=216`
`a+a^(2)+3a*6=216`
`a^(2)+19a-216=0or a=8,a=-27`
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Comprehension)|6 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Single)|23 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

  • PARABOLA

    CENGAGE|Exercise Question Bank|9 Videos

Similar Questions

Explore conceptually related problems

If the equation kx^(2) – 2xy - y^(2)– 2x + 2y = 0 represents a pair of lines, then k =

The equation x^(2) + y^(2) + 2gx + 2fy + c=0 reprsents the circle if

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

If the equation p x^2+(2-q)x y+3y^2-6q x+30 y+6q=0 represents a circle, then find the values of pa n dqdot

9x^(2) +2hxy +4y^(2) +6x +2fy - 3 = 0 represents two parallel lines. Then

If the equation 2x^2+k x y+2y^2=0 represents a pair of real and distinct lines, then find the values of kdot

Show that 4x^(2)+4xy+y^(2)-6x-3y-4=0 represents a pair of parallel lines.

Show that the equation 4x^(2)+4xy+y^(2)-6x-3y-4=0 represents a pair of parallel lines. Find the distance between them.