Orthogonality of Two Circles
Trending Questions
Q. If the two circles 2x2+2y2−3x+6y+k=0 and x2+y2−4x+10y+16=0 cut orthogonally, then the value of k is .
- 4
- 10
- 1
- 5
Q.
x2+y2+px+3y−5=0 and x2+y2+5x+py+7=0 cuts orthogonally, then P is _______
12
1
32
2
Q. If the two circles, which pass through (0, a) and (0, −a) and touch the line y=mx+c, will cut orthogonally, if
- c2=a2(2−m2)
- a2c2=12+m2
- c2=a2(2+m2).
- c2=a2(1−m2).
Q. The members of a family of circles are given by the equation 2(x2+y2)+λx−(1+λ2)y−10=0. The number of circle(s) from this family that is/are cut orthogonally by the circle x2+y2+4x+6y+3=0 is
- 2
- 1
- 0
- infinite
Q. The equation of the circle which cuts orthogonally each of the three circles given below:
x2+y2−2x+3y−7=0, x2+y2+5x−5y+9=0 and x2+y2+7x−9y+29=0
x2+y2−2x+3y−7=0, x2+y2+5x−5y+9=0 and x2+y2+7x−9y+29=0
- x2+y2−16x−8y−12=0
- x2+y2−16x−18y−4=0
- x2+y2+16x−18y+4=0
- x2+y2+16x+18y+12=0
Q. The locus of the centre of the circle which cuts x2+y2−20x+4=0 orthogonally and touches the line x=2, is
- y2=4(4x+1)
- y2=16x
- x2=4(4y+1)
- y2=−16x
Q.
How do you find the equation of a circle center of and a radius of ?
Q. The equation of circle touching the line 2x+3y+1=0 at (1, −1) and orthogonally cutting the cirlce whose endpoints of diameter are (0, 3) and (−2, −1) is
- 2x2+2y2+10x+5y+1=0
- 2x2+2y2−10x−5y+1=0
- 2x2+2y2−10x−10y+10=0
- 2x2+2y2−10x−10y+20=0
Q. A circle S passes through the point (0, 1) and is orthogonal to the circles (x−1)2+y2=16 and x2+y2=1. Then
- Radius of S is 8
- Radius of S is 7
- Centre of S is (−7, 1)
- Centre of S is (−8, 1)
Q. The equation of circle touching the line 2x+3y+1=0 at (1, −1) and cutting orthogonally the circle having line segment joining (0, 3) and (−2, −1) as diameter is
- 2x2+2y2−10x−10y+10=0
- 2x2+2y2−10x−10y+20=0
- 2x2+2y2−10x−5y+1=0
- 2x2+2y2+10x+5y+1=0
Q. The equation of circle touching the line 2x+3y+1=0 at (1, −1) and cutting orthogonally the circle having line segment joining (0, 3) and (−2, −1) as diameter is
- 2x2+2y2+10x+5y+1=0
- 2x2+2y2−10x−5y+1=0
- 2x2+2y2−10x−10y+10=0
- 2x2+2y2−10x−10y+20=0
Q. If a circle passes through the point (a, b) and cuts the circle x2+y2=4 orthogonally, then the locus of its centre is
- 2ax+2by+(a2+b2+4=0)
- 2ax+2by−(a2+b2+4)=0
- 2ax−2by−(a2+b2+4)=0
- 2ax−2by−(a2+b2+4)=0
Q. The circle C1:x2+y2=8 cuts orthogonally the circle C2 whose centre lies on the line x−y−4=0 then, the circle C2 passes through a fixed point, which lies on
- x−2y=0
- x+y=0
- x−2y=0
- x+2y=0