Circle

Question 1

Concentric Circles

Answer 1

Circles having same centre

Question 2

Congruent Circles

Answer 2

Circles having same radius

Question 3

What is the centre-radius form of the circle?

Answer 3

(x-a)^2 + (y-b)^2 =r^2

Question 4

Point circle

Answer 4

Circle having radius 0

Question 5

General Equation of Circle

Answer 5

x^2+y^2+2gx+2fy+c=0

Question 6

What is the conditions of circle?

Answer 6

Coefficient of x^2=Coefficient of y^2 =1
Coefficient of xy = 0

Question 7

Centre of the circle and radius

Answer 7

Centre = (-g, -f)
Radius = root(g^2+f^2-c)

Question 8

Diametrical Form of circle

Answer 8

(x-x1)(x-x2) + (y-y1)(y-y2)=0

Question 9

Parametric Form

Answer 9

x=x1 + rcosθ
y = y1 +rsin

Question 10

Conditions of tangency

Answer 10

OP = r, where r=radius of circle

Question 11

Equation of tangent replacement for T=0

Answer 11

x^2=xx1
y^2=yy1
x=(x+x1)/2
y = (y+y1)/2
xy = (x1y+xy1)/2
c = c

Question 12

Length of external tangent as power of a point

Answer 12

root s1, where s1 is the power of external point from which tangents are drawn from

Question 13

Equation of chord of contact

Answer 13

T=0

Question 14

Equation of a pair of tangents

Answer 14

Ss1 = T^2
where S = Equation of circle
S1 = Power of a point
T = Replacement

Question 15

Equation of chord with a given middle point

Answer 15

T=S1

Question 16

Director Circle

Answer 16

Locus of point of intersection of mutually perpendicular tangents to a given curve where the radius of the director circle is root 2 times the radius of circle

Question 17

Orthogonal Circle

Answer 17

If the angle of intersection is 90 degree, then the circles are said to be orthogonal to each other

Question 18

Conditions of orthogonality

Answer 18

2g1g2 + 2f1f2 = c1+c2

Question 19

Radical Axis

Answer 19

Locus of a point such that the tangent drawn from it on the circles are equal in length