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 $m=k=-1,n=1$