# eccentricity of locus of circle

A circle cuts two fixed perpendicular lines such that each of the non zero intercept is of given length (but unequal).Now we have to prove the eccentricity of locus of the centre of the circle is $\sqrt2$ .

• What are the two lengths? – Qwerty Dec 17 '16 at 18:59

Let $(x,y)$ be the centre of the circle.
WLOG, take the two perpendicular lines to be the $X$ and $Y$ axes.
$$y^2+a^2=x^2+b^2$$
Where $a$ and $b$ are the two sub segments(=segment length/2)
• @user123733 Assume $2b$ to be the intercept on the $Y$ axis and $2a$ to be on the $X$ axis. (2 perpendicular lines). Sum of squares =radius$^2$ – Qwerty Dec 18 '16 at 4:06
• Why sum of squares = radius$^2$ – user123733 Dec 18 '16 at 4:23