Question

A line segment of length (a + b) moves in such a way that its ends are always on two fixed perpendicular straight lines. Then the locus of the point on this line which divide it into portions of lengths a and b is-

• A. A parabola
• B. A circle
• C. An ellipse
• D. None of these

Answer 1

Answer: (C)

An ellipse

Answer 2

a² + b² = (a + b)²

h = $\frac{b\alpha}{a + b}$ Ž a = $\frac{h(a + b)}{b}$

k = $\frac{a\beta}{a + b}$ Ž b = $\frac{k(a + b)}{a}$

$\frac{h^{2}(a + b)^{2}}{b^{2}}$ + $\frac{k^{2}(a + b)^{2}}{a^{2}}$ = (a + b)²

locus of (h, k) is

$\frac{x^{2}}{b^{2}}$ + $\frac{y^{2}}{a^{2}}$ = 1, ellipse