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MHT-CET : Mathematics Entrance Exam

MHT - CET : Mathematics - Circle Formulae Page 1

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 1. Equation of a circle in the centre radius form

 

(x - h)2 + (y - k)2 = a2

where,

radius is '
a' and centre is c(h, k).

 

 2. Equation of a circle in the diameter form

 

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

where,

A(
x1, y1) and B(x2, y2) are the extremities of the diameter.

 

 3. General equation of a circle

 

x2 + y2 + 2gx + 2fy + c = 0

where,
centre is (
- g, - f) and radius =

 

 4. Parametric equations of a circle

 

x = a cosq, y = a sinq are the parametric equations of the circle

x2 + y2 = a2.

 

5. Circles touching internally and externally

 

 

If x2 + y2 + 2g1 x + 2f1 y + c1 = 0 and

x2 + y2 + 2g2x + 2f2 y + c2 = 0 are the

equations of the two circles touching one another,
then their centres are given by
C1 (- g1, - f1), C2 (- g2, - f2) and their radii are
r1 = , r2 =

 

 

6. Equation of the tangent to a circle with origin as centre

 

 

The equation of the tangent to the circle
x
2 + y2 = a2 at a point P(x1, y1) on it is given as xx1 + yy1 = a2,
where
P(
x1, y1) is a point in the circle and the tangent and 'a' is the radius.

 

7. Equation of the tangent to a circle at a point (x1, y1)

 

 

The equation of the tangent to the circle
x
2 + y2 + 2gx + 2fy + c = 0 at a point P (x1, y1) on it is
xx1 + yy1 + g(x + x1) + f(y + y1) + c = 0

 

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