Saya mau tau Contoh kedua dari Lokus (matematika)

A triangle ABC has a fixed side [AB] with length c.

Determine the locus of the third vertex C such that

the medians from A and C are orthogonal.

Choose an orthonormal coordinate system such that A(−c/2, 0), B(c/2, 0).

C(x, y) is the variable third vertex. The center of [BC] is M((2x + c)/4, y/2). The median from C has a slope  y/x. The median AM has slope  2y/(2x + 3c).

C(x, y) is a point of the locus

the medians from A and C are orthogonal

The locus of the vertex C is a circle with center (−3c/4, 0) and radius 3c/4.