MHT-CET : Mathematics Entrance Exam

### MHT - CET : Mathematics - Circle Formulae Page 2

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8. Equation of a tangent at parametric point

 The equation of the tangent to the circle x = a cos q, y = a sin q at a point P(q) on it is x cos q + y sin q = a

9. Length of the tangent segment to the circle

 The length of the tangent segment to the circle x2 + y2 + 2gx + 2fy + c = 0 drawn from a point P(x1, y1) outside the circle is given by PT =

10. Condition that the line lx + my + n = 0 is tangent to a circle

 The condition that the line lx + my + n = 0 is a tangent to the circle x2 + y2 + 2gx + 2fy + c = 0 is (n - lg - mf)2 = (l2 + m2) (g2 + f2 - c)

11. Condition of tangency

 c = ± a is called the condition of tangency for the line y = mx + c to be a tangent to a circle x2 + y2 = a2.

12. Point of contacts of the tangents to a circle x2 + y2 = a2

 P º ( - a2m , a2 ) , where c = ± a c c

13. Locus of a point

 The locus of a point, the tangents from which to the circle x2 + y2 = a2 are mutually perpendicular, is given as x2 + y2 = 2a2.

14. Angle between tangents

 To find the acute angle between the tangents drawn to the circle, you can use the formula tan q =, where m1 and m2 are the slopes of tangents.

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