Question

If x/b = y/a, bx + ay = a² + b², then the values of (x, y) are ……………. 

A) (a, b) 

B) (a, -b) 

C) (b, -a)

D) (b, a)

Answer 1

Correct option is (D) (b, a)

Given that \(\frac{x}{b}=\frac{y}{a}\)

\(\Rightarrow\) ax = by     (By cross multiplication)

\(\Rightarrow\) ax - by = 0                 ___________(1)

And \(bx+ay = a^2+b^2 \)    ___________(2)

Put \(x=\frac{by}a\) from (1) into (2), we get

\(\frac{b^2y}a+ay=a^2+b^2\)

\(\Rightarrow\) \((b^2+a^2)y=(a^2+b^2)a\)

\(\Rightarrow y=\frac{(a^2+b^2)a}{a^2+b^2}=a\)

\(\therefore x=\frac{by}a=\frac{ba}a=b\)

Hence, (x, y) = (b, a)

Answer 2

Correct option is D) (b, a)