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 º (- g1, - f1), C2 º (- 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 x2 + 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 x2 + 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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