Question

The locus of a variable point whose distance from (- 2, 0) is \[\frac{2}{3}\] times its distance from the line \[x=-\frac{9}{2}\], is______.

Options

• Ellipse

• Parabola

• Hyperbola

• None of these

Answer 1

Ellipse

Explanation:

This uses the focus-directrix definition of a conic:

\[e=\frac{\text{distance from focus}}{\text{distance from directrix}}=\frac{2}{3}\]

Since \[e=\frac{2}{3}\] < 1, the conic is an Ellipse.