‹‹ Previous | Page 1 | Page 2 | Next ››

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} + y^{2} + 2gx + 2fy + c = 0 drawn from a point P(x_{1}, y_{1}) 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} + y^{2} + 2gx + 2fy + c = 0 is (n - lg - mf)^{2} = (l^{2} + m^{2}) (g^{2} + f^{2} - 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 x^{2} + y^{2} = a^{2}.

12. Point of contacts of the tangents to a circle x^{2} + y^{2} = a^{2}

P º

(

- a^{2}m

,

a^{2}

)

, where c = ± a

c

13. Locus of a point

The locus of a point, the tangents from which to the circle x^{2} + y^{2} = a^{2} are mutually perpendicular, is given as x^{2} + y^{2} = 2a^{2}.

14. Angle between tangents

To find the acute angle between the tangents drawn to the circle, you can use the formula tan q =, where m_{1} and m_{2} are the slopes of tangents.