Home
Class 12
MATHS
Let the lines (y-2)=m1(x-5) and (y+4)=m2...

Let the lines `(y-2)=m_1(x-5)` and `(y+4)=m_2(x-3)` intersect at right angles at `P` (where `m_1 and m_2` are parameters). If the locus of `P` is `x^2+y^2+gx+fy+7=0` , then the value of `|f+g|` is__________

Text Solution

Verified by Experts

The correct Answer is:
6
Clearly, the locus of the point of intersection of lines is
`(x-5)(x-3) +(y-2) (y+4) =0`
or `x^(2)+y^(2)-8x+2y+7=0`
Hence, `|f +g| = | 2 + (-8) | = 6`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CIRCLE

    CENGAGE ENGLISH|Exercise ARCHIVES (JEE MAIN)|1 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|9 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise For Problems|43 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

Let the lines (y-2)=m_(1)(x-5) and (y+4)=m_(2)(x-3) intersect at right angles at P (where m_(1) and m_(2) are parameters). If locus of P is x^(2)+y^(2)+gx+fy+7=0 , then ((g)/(2))^(2)+((f)/(2))^(2)-7 is equal to

Two straight lines (y-b)=m_1(x+a) and (y-b)=m_2(x+a) are the tangents of y^2=4a xdot Prove m_1m_2=-1.

Knowledge Check

  • The lines with the equations y = m_(1)x+4 and y = m_(2)x+3 will intersect to the right of the y - axis if and only is

    A
    `m_(1)=m_(2)`
    B
    `m_(1)lt m_(2)`
    C
    `m_(1)gt m_(2)`
    D
    `m_(1)+m_(2)=0`

    • Similar Questions

    Explore conceptually related problems

    Two straight lines (y-b)=m_1(x+a) and (y-b)=m_2(x+a) are the tangents of y^2=4a xdot Prove m_1m_2=-1.

    If the line y=m x+1 is tangent to the parabola y^2=4x , then find the value of m .

    If the angle between the two lines represented by 2x^2+5x y+3y^2+6x+7y+4=0 is tan^(-1)(m), then find the value of m .

    If the angle between the two lines represented by 2x^2+5x y+3y^2+6x+7y+4=0 is tan^(-1)(m), then find the value of mdot

    The line y=m x bisects the area enclosed by the curve y=1+4x-x^2 and the lines x=0,x=3/2 and y=0. Then the value of m is

    Find the condition for the line y=m x to cut at right angles the conic a x^2+2h x y+b y^2=1.

    Let the tangents to the parabola y^(2)=4ax drawn from point P have slope m_(1) and m_(2) . If m_(1)m_(2)=2 , then the locus of point P is

    Home
    Profile