Question

Write the condition that Ix + my + n = 0 may be a tangent to the circle x²+y² + 2gx + 2fy +C =0

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Answer 1

`r= \frac { \sqrt{ {l}^(2) + {m}^(2) } }`

Explanation:

The given circle has equation

`{x}^(2) + {y}^(2) + 2gx + 2fy + c = 0`

This circle has centre (-g,-f).

For the line

`lx + my + n = 0`

to be a tangent to this circle, the perpendicular distance from the center to this line must be equal to the radius of the circle.

This is given by:

`d = \frac { \sqrt{ {a}^(2) + {b}^(2) } }`

We substitute the center and radius to get:

`r=\frac { \sqrt{ {l}^(2) + {m}^(2) } }`

We simplify to get;

`r= \frac { \sqrt{ {l}^(2) + {m}^(2) } }`