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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
x
2 + 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

x
2 + 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  

(

- a2m

,

a2

)

, where c = a

c

c

 

13. Locus of a point

 

The locus of a point, the tangents from which to the circle

x
2 + 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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