Show that the curves `x y=a^2a n dx^2+y^2=2a^2`touch each other

1.	Show that the curves `x y=a^2a n dx^2+y^2=2a^2`touch each other
Answer» curves are `xy= a^2` `x^2 + y^2 = 2a^2` `x^2 + (a^2/x)^2 = 2a^2` `x^2 + a^4/x^2 = 2a^2` `x^4 + a^4 = 2a^2x^2` `x^4 + a^4 = 2a^2x^2` `x^4 + a^4 - 2a^2x^2 = 0` `(x^2 - a^2)^2 = 0` `x^2 = a^2` `x= +- a` now,`xy= a^2` `xdy/dx + y(1) = 0` `dy/dx = -y/x = -a/a= m_1` now, `x^2 + y^T2 = 2a^2` `2x + 2y dy/dx= 0` `dy/dx= -x/y=-a/a= -1= m_2` as,`m_1=m_2` so, curves are touching each other hence proved

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Show that the curves `x y=a^2a n dx^2+y^2=2a^2`touch each other

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