Question

If AB = 2a, given the base of DABP, where P is a variable such that tanA + tanB = l (constant), then the locus of P is-

• A. A circle
• B. A parabola
• C. A hyperbola
• D. None

Answer 1

Answer: (B)

A parabola

Answer 2

tan A = $\frac{y}{a - x}$; tan B = $\frac{y}{a + x}$

tan A + tan B = l

$\frac{y}{a - x}$ + $\frac{y}{a + x}$ = l Ž $\frac{y.2a}{a^{2} - x^{2}}$= l

a² – x² = $\frac{2a}{\lambda}$y Ž x² = a² – $\frac{2a}{\lambda}y$ Parabola.