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.