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Grade 11Algebra

if x=4 λ/(1+λ^2) and y=2-2 λ^2/1+λ^2 where λ is a real parameter then x^2-xy+y^2 lies between [a,b] then (a+b) is

Profile image of Mili
9 Years agoGrade 11
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1 Answer

Profile image of jagdish singh singh
9 Years ago
\hspace{-0.8 cm}$ Given $x=\frac{4\lambda}{1+\lambda^2}$ and $y=\frac{2(1-\lambda)}{1+\lambda^2}\;,$ Then $x^2+y^2=4$\\\\Now put $x=u+v$ and $y=u-v\;,$ We get $u^2+v^2=2$\\\\and $f(x,y) =x^2+y^2-xy=3u^2+v^2$\;, Now parametric equation of \\\\$x^2+y^2=2$ is $x=\sqrt{2}\cos \phi$ and $y=\sqrt{2}\sin \phi.$ \\\\So $f(\phi)=4\cos^2 \phi+2\;, $So we get $f(\phi)\in \left[4,6\right]$

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