Circles

Question 1

What is the simplest equation of a circle?

Answer 1

x^2 + y^2= r^2

Question 2

What is the equation of a circle with centre (a,b) and radius r

Answer 2

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

Question 3

What is the general question of 2 degree?

Answer 3

ax^2+2hxy+by^2+2gx+2fy+c=0

Question 4

What is the general equation of the circle ?

Answer 4

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

Where g,f and c are constants.

Question 5

What are the coordinates of centre and radius of the circle from its general equation?

Answer 5

Coordinates of centre
(-g,-f)
Radius of circle
(g^2+f^2-c)^1/2

Question 6

What is the equation of circle with A(X1,Y1) and

B(X2,Y2) as ends of the diameter?

Answer 6

(X-X1)(X-X2)+(Y-Y1)(Y-Y2)=0 is the required equation.

Question 7

What is the parametric equation of the circle of equation (x-h)^+(y-k)^=a^ ?

Answer 7

x=h+a cos #

y=k+a sin #

Question 8

What is the equation of tangent to the circle x^+y^=r^ ?

Answer 8

T=xx1+yy1-r^=0

Question 9

What is the equation of tangent to the circle (x-h)^+(y-k)^=r^

Answer 9

T=(x-h)(x1-h)+(y-k)(y1-k)-r^=0

Question 10

What is the equation of tangent to the circle x^+y^+2gx+2fy+c=0 ?

Answer 10

T=xx1+yy1+g(x+x1)+f(y+y1)+c=0

Question 11

What is the equation of tangent to circle x^+y^=r^ in slope form.

Answer 11

y=mx+r[(1+m^)^1/2)]