Home
Class 12
MATHS
The line Ax+By+C=0, cuts the circle x^(2...

The line `Ax+By+C=0`, cuts the circle `x^(2)+y^(2)+ax+by+c=0` in P and Q and the line `A'x+B'y+C'=0` cuts the circle `x^(2)+y^(2)+dx+b'y+c'=0` in R and S. If the four points P,Q,R,S are concyclic, then
`D=|(a-a',b-b',c-c'),(A,B,C),(A',B',C')|=0`

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THE CIRCLE

    ML KHANNA|Exercise Problem Set (7) (MULTIPLE CHOICE QUESTIONS) |23 Videos

  • THE CIRCLE

    ML KHANNA|Exercise Problem Set (7) (TRUE AND FALSE) |3 Videos

  • THE CIRCLE

    ML KHANNA|Exercise Problem Set (6) (MULTIPLE CHOICE QUESTIONS) |27 Videos

  • TANGENTS AND NORMALS

    ML KHANNA|Exercise SELF ASSESSMENT TEST (MULTIPLE CHOICE QUESTIONS)|19 Videos

  • THE ELLIPSE

    ML KHANNA|Exercise SELF ASSESSMENT TEST|9 Videos

Similar Questions

Explore conceptually related problems

The line Ax+By+=0 cuts the circle by x^2+y^2+Ax+By+C=0at P and Q. The line A'x +B'x+C'=0 cuts the circle x^2+y^2+a'x+b'y+c'=0 at R and S.If P,Q, R and S are concyclic then show that det (( a-a", b-b',c-c'),(A,B,C),(A',B',C'))=0

A line y=2x+c intersects the circle x^(2)+y^(2)-2x-4y+1=0 at P and Q. If the tangents at P and Q to the circle intersect at a right angle,then |c| is equal to

Knowledge Check

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

    A
    ag+bf+c=0
    B
    ag+bf+-c=0
    C
    ag-bf+c=0
    D
    ag-bf-c=0

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

    A
    ag+bf+c=0
    B
    ag+bf-c=0
    C
    ag-bf+c=0
    D
    ag-bf-c=0

  • The line ax +by+c=0 is an normal to the circle x^(2)+y^(2)=r^(2) . The portion of the line ax +by +c=0 intercepted by this circle is of length

    A
    `sqrtr`
    B
    r
    C
    `r^(2)`
    D
    2r

    • Similar Questions

    Explore conceptually related problems

    Line x/a+y/b=1 cuts the coordinate axes at A(a,0) and B(0,0) and the line x/a+y/b= -1 at A'(-a',0) and B'(0,-b') . If the points A,B A' ,B' are concyclic , then the orthocentre of the triangle ABA' is

    The line 2x-y+4=0 cuts the parabola y^(2)=8x in P and Q. The mid-point of PQ is (a) (1,2)(b)(1,-2)(c)(-1,2)(d)(-1,-2)

    If the circles x^(2)+y^(2)+2ax+c=0 and x^(2)+y^(2)+2by+c=0 touch each other,then find the relation between a,b and c.

    If the line ax +by+c = 0 where a, b, c inR and a, b,c notin 0 is a normal to the curve y=x^(2) , then x^(3)+2a^(2)x+4a^(2)c = 0 has

    If the line x+y=0 touches the curve y=x^(2)+bx+c at the point x=-2 , then : (b,c)-=

    Home
    Profile