The number of tangents which can be drawn from the point (–1,2) to the circle $x^{2} + y^{2} + 2 x - 4 y + 4 = 0$ is

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Solution

We'll check the position of the point through $S_{1}$ .
$S_{1}$ = $(- 1)^{2} + (2)^{2} + 2 (- 1) - 4 (2) + 4 = 0$
= -1
Since it's negative the point lies within the circle, and hence no tangent can be drawn.

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