Question

Chords of an ellipse are drawn through the positive end of the minor axis. Then locus of mid point of chords must be

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

Answer 1

Answer: (C)

An ellipse

Answer 2

$\frac{x^{2}}{a^{2}}$+ $\frac{y^{2}}{b^{2}}$ = 1;equation of chord in mid-point

form T= S₁

$\frac{hx}{a^{2}}$ + $\frac{ky}{b^{2}}$ – 1 = $\frac{h^{2}}{a^{2}} + \frac{k^{2}}{b^{2}}$ – 1

it is passes through (0, b) ; 0 + $\frac{k}{b}$ = $\frac{h^{2}}{a^{2}}$ + $\frac{k^{2}}{b^{2}}$

locus of (h, k) is $\frac{x^{2}}{a^{2}}$ + $\frac{y^{2}}{b^{2}}$ – $\frac{y}{b}$ = 0

which is again a ellipse.