Home › Forums › Math questions › Geometry questions

Parabola

Posted February 2nd, 2010 by alpha
in

Find the locus of the middle points of all the chords of the parabola y^2=4ax which are drawn through the vertex.

‹ Parabola-3 parabola-2 ›

Comments

answer

On February 3rd, 2010 Structure says:

Equations $ y=m(x-a) $ $ y^2=4ax $ give

$$m^2x^2-2am^2x-4ax+m^2a^2=0$$
$$x_0=\frac{1}{2}(x_1+x_2)=a\frac{m^2+2}{m^2}=a+\frac{2a}{m^2}$$
$$y_0=\frac{2a}{m}$$
$$x_0=a+\frac{y_0^2}{2a}$$

Back to top