Question

Upon $X-Y$ plane, the path defined by the equation $\frac{1}{x^m}+\frac{1}{y^m}+\frac{k}{(x+y)^n}=0$ is

• A. a parabola if $m =-\frac{1}{2}, k =-1, n =0$
• B. a hyperbola if $m =1, k =-1, n =0$
• C. a pair of lines if $m = k = n =1$
• D. a pair of lines if $m = k =-1, n =1$

Answer 1

Answer: (A), (B), (C), (D)

Correct answer is (a) a parabola if $m =-\frac{1}{2}, k =-1, n =0$Correct answer is (b) a hyperbola if $m =1, k =-1, n =0$Correct answer is (c) a pair of lines if $m = k = n =1$Correct answer is (d) a pair of lines if $m = k =-1, n =1$