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.

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