Question

Let a, b, x, y be real numbers such that \(a^2+b^2=25,x^2+y^2=169,\) and \(ax+by=65.\) If \(k= ay-bx,\) then

• A. k=0
• B. \(0<k≤\frac{5}{13}\)
• C. \(k=\frac{5}{13}\)
• D. \(k>\frac{5}{13}\)

Answer 1

The Correct Option is A

We can take \(a=5, b=0, x=13\) and \(y=0\) as values which satisfies all three equations.

Hence, \(k=ay−bx=5×0−0×13=0\)