# Intercepts Cut by the Circle on Axes

Here you will learn intercept cut by the circle an the axes i.e. x-axis and y-axis respectively.

Let’s begin –

## Intercept Cut by Circle on Axes

The intercepts cut by the circle $$x^2 + y^2 + 2gx + 2fy + c$$ = 0 on :

#### (i) x-axis

x-axis = 2$$\sqrt{g^2 – c}$$

#### (ii) y-axis

y-axis = 2$$\sqrt{f^2 – c}$$

Note :

(i)  If the circle cuts the x-axis at two distinct points, then $$g^2 – c$$ > 0

(ii)  If the circle cuts the y-axis at two distinct points, then $$f^2 – c$$ > 0

(iii)  If circle touches x-axis then $$g^2$$ = c.

(iv)  If circle touches y-axis then $$f^2$$ = c.

(v)  Circle lies completely above or below the x-axis then $$g^2$$ < c.

(vi)  Circle lies completely to the right or left to the y-axis, then $$f^2$$ < c.