Home
Class 12
MATHS
Find the limiting points of the circles ...

Find the limiting points of the circles `(x^(2)+y^(2)+2gx+c)+lamda(x^(2)+y^(2)+2fy+d)=0` and show that the square of the distance between them is
`(( c-d)^(2)-4f^(2)g+4cf^(2)+4dg^(2))/(f^(2)+g^(2))`

Text Solution

Verified by Experts

The correct Answer is:
`([( c-d)^(2)-4f^(2)g+4cf^(2)+4dg^(2)])/(f^(2)+g^(2))`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|18 Videos

  • CIRCLE

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|17 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS ENGLISH|Exercise Complex Number Exercise 8|2 Videos

Similar Questions

Explore conceptually related problems

If the two circles x^(2)+y^(2)+2gx+c=0 and x^(2)+y^(2)-2fy-c=0 have equal radius then locus of (g,f) is

The circle x^(2) + y^(2) + 2g x + 2fy + c = 0 does not intersect the y-axis if

If two circle x^(2)+y^(2)+2gx +2fy=0 and x^(2)+y^(2)+2g'x+2f'y=0 touch each other then proove that f'g =fg'.

For the circle x^(2)+y^(2)-4x+2y+c=0 radius is 4 then c=

Find the locus of the mid-point of the chords of the circle x^2 + y^2 + 2gx+2fy+c=0 which subtend an angle of 120^0 at the centre of the circle.

The equation of the tangent to circle x^(2)+y^(2)+2g x+2fy=0 at origin is :

If O is the origin and OP, OQ are distinct tangents to the circle x^(2)+y^(2)+2gx+2fy+c=0 then the circumcentre of the triangle OPQ is

One of the limit point of the coaxial system of circles containing x^(2)+y^(2)-6x-6y+4=0, x^(2)+y^(2)-2x-4y+3=0 , is

The line ax+by+by+c=0 is normal to the circle x^(2)+y^(2)+2gx+2fy+d=0, if

If PQ, PR are tangents from a point P(x_(1),y_(1)) to the circle x^(2)+y^(2)+2gx+2fy+c=0 show that the circumcircle of the triangle PQR is (x-x_(1))(x+g)+(y-y_(1))(y+f)=0