Home
Class 12
MATHS
If the sum of the slopes of the lines gi...

If the sum of the slopes of the lines given by `x^2-2c x y-7y^2=0` is four times their product, then the value of `c` is_____

Text Solution

Verified by Experts

Given equation of pair of lines is `x^(2)-2cxy-7y^(2)=0` .
Let the slopes of the component lines be `m_(1)andm_(2)`. It is given that
`m_(1)+m_(2)=4m_(1)m_(2)`
`rArr-(2c)/(7)=(-4)/(7)`
`:.c=2`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Illustration 3.12|1 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Illustration 3.13|1 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Illustration 3.10|1 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|6 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Matching Column Type|1 Videos

Similar Questions

Explore conceptually related problems

If sum of the slopes of the lines x^2+kxy-3y^2=0 is twice the product of the slopes,then find the value of k.

If the gradient of one of the lines x^(2)+hxy+2y^(2)=0 twice that of the other , then sum of possible values of h ____________.

Knowledge Check

  • If the straight line joining the point (0, 3) and (5, -2) is a tangent to the curve y(x+1)=c , then the value of c will be-

    A
    3
    B
    -3
    C
    4
    D
    -4

    • Similar Questions

    Explore conceptually related problems

    If the line x+2b y+7=0 is a diameter of the circle x^2+y^2-6x+2y=0 , then find the value of b .

    If the lines x+(a-1)y+1=0 and 2x+a^2y-1=0 are perpendicular, then find the value of adot

    If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisector of the angle between the other two, then the value of c is

    If the sum of the slopes of the normal from a point P to the hyperbola x y=c^2 is equal to lambda(lambda in R^+) , then the locus of point P is (a) x^2=lambdac^2 (b) y^2=lambdac^2 (c) x y=lambdac^2 (d) none of these

    The sum of the slopes of the lines tangent to both the circles x^2+y^2=1 and (x-6)^2+y^2=4 is________

    If the staight line x+ y= c touches the circlc x^2 + y^2= 2 , then the value of |c| is

    The equations of a line which is parallel to the line common to the pair of lines given by 6x^(2)-xy-12y^(2)=0and15x^(2)+14xy-8y^(2)=0 and the sum of whose intercepts on the axes is 7, is :

    Home
    Profile