Question

PM and PN are the perpendiculars from any point on a rectangular hyperbola to its asymptotes. If Q divides MN in the ratio 3 : 1, then the locus of Q is-

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

Answer 1

Answer: (D)

A rectangular hyperbola

Answer 2

If the R.H. is xy = c2. then P is

(ct, $\frac{c}{t}$

M = (ct, 0); N = $\left( 0,\frac{c}{t} \right)$

Q = $\left( \frac{ct}{4},\frac{3c}{4t} \right)$ = (x, y)

\ xy =$\frac{3c^{2}}{16}$ which is another R.H.