Equation of normal:

The normal at any point of the curve is straight line which is perpendicular to the tangent at point of tangency (point of contact).

Normal of any circle always passes through centre of circle.

The equation of normal to the circle x²+y²+2gx+2fy+c=0 at any point (x₁, y₁) lying on the circle is 

length of the tangent

The length of tangent drawn from the point (x₁, y₁) outside circle S º 0, to circle is √S₁.

Position of a point with respect to a circle:

Let equation of given circle be x²+y²+2gx+2fy+c=0 and the given point be P(a,b). Now, If distance of the point P(a,b) from centre of the circle(O) is greater than the radius of the circle that is PO > √(g² + f² - C),  then the point will lie outside the circle.

=>  > 0, point P will lie outside circle.

Similarly

If  = 0, point P will lie outside circle.

If   <0 0, point P will lie outside circle.

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