Question

If on a given base triangle b be described such that the sum of the tangents of the base angles is constant (k), then the locus of third vertex is –

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

Answer 1

Answer: (D)

A parabola

Answer 2

Let AB is the given base.

tan A + tan B = k

tan A = $\frac { \beta } { \alpha }$, tan B =

Now, $\frac { \beta } { \alpha }$ – $\frac { \beta } { \alpha - \mathrm { a } }$ = k

Ž –ab = k (a² – aa)

Ž x² = – $\frac { \mathrm { a } } { \mathrm { k } }$ y + ax

Which is equation of a parabola

Hence (4) is correct answer.