Question

Two straight lines pass through the fixed points (± a, 0) and have slopes whose products is p > 0. Then, the locus of the points of intersection of the lines is

(a) a circle

(b) a parabola

(c) an ellipse

(d) a hyperbola

Answer 1

The correct option (d) a hyperbola

Explanation:

Let lines be y = m1(x – a) and y = m2(x + a)

also m1 ∙ m2 = p > 0

∴ y2= m1m2(x2 – a2) locus of point of intersection

∴ y2 = p(x2 – a2).

or px2 – y2 = pa2

This is equation of hyperbola.