Question

If the base of triangle is given and ratio of tangent of half the base angles is constant, then locus of vertex of the triangle is

• A. circle
• B. parabola
• C. ellipse
• D. hyperbola

Answer 1

Answer: (D)

hyperbola

HYPERBOLA

BC be the base of the triangle.

$|\overline{AC}|-|\overline{AB}|=(a+c)-(a+b)=c-b=|\overline{CP}|-|\overline{BP}|$

So, the locus of A is the hyperbola with foci B and C, and with the constant difference of distances.