Radical Axis
Trending Questions
Q.
The equation of the common chord of the circles (x−a)2+(y−b)2=c2 and (x−b)2+(y−a)2=c2 is
x−y=0
x+y=0
x+y=a2+b2
x−y=a2−b2
Q. If the radical axis of the circles x2+y2+2gx+2fy+c=0 and 2x2+2y2+3x+8y+2c=0 touches the circle x2+y2+2x+2y+1=0, Then
- g=34 or f=−2
- g=14 or f=2
- g=−34 or f=−1
- g=34 or f=2
Q. Consider three circles whose equations are x2+y2+3x+2y+1=0, x2+y2−x+6y+5=0 and x2+y2+5x−8y+15=0, then
- radical centre of the circles is (3, 2)
- equation of the circle which is orthogonal to given circles isx2+y2−6x−4y−14=0
- equation of the circle which is orthogonal to given circles isx2+y2−6x+4y−13=0
- radical centre of the circles is(3, −2)
Q. General value of θ satisfying the equation tan2θ+sec2θ=1 is/are
Q.
If the circles x2+y2+2ax+cy+a=0 and x2+y2−3ax+dy−1=0 interesect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for
(2005)
exactly for one value of a
no value of a
infinitely many values of a
exactly two values of a
Q. If a variable line y = 2x + p lies between the circles x2+y2−2x−2y+1=0 and x2+y2−16x−2y+61=0 without intersecting or touching either circles, then number of integral values of p is
- 9
- 8
- 7
- 6
Q. Conisder the circle x2+y2−10x−6y+30=0. Let O be the centre of the circle and tangent at A(7, 3) and B(5, 1) meet at C. Let S=0 represents family of circles passing through A and B, then
- Area of quadrilateral OACB=4sq units
- The radical axis for the family of circles S=0 is x+y=10
- The smallest possible circle of the family S=0 is x2+y2−12x−4y+38=0
- The coordinates of point C are (7, 1)
Q. The radical axis of the circles x2+y2+4x−6y−12=0 and x2+y2+2x−2y−1=0 divides the line segment joining the centres of the circles in the ratio
- 27:17
- 3:7
- −27:17
- −3:7
Q. If the length of the tangents from (a, b) to the circles x2+y2−4x−5=0 and x2+y2+6x−2y+6=0 are equal then 10a−2b is equal to
- 10
- −11
- 11
- −10