Question

Question #2590e

Answer 1

`x^2+y^2=a^2+b^2` which is a circle centered at the origin, with radius `sqrt(a^2+b^2)`

Explanation:

Solving for `x,y`

`{(y+mx=sqrt(a^2m^2+b^2)),(my-x=sqrt(a^2+b^2m^2)):}`

we have

`{(x = (m sqrt[b^2 + a^2 m^2] - sqrt[a^2 + b^2 m^2])/(1 + m^2)),(y=(sqrt[b^2 + a^2 m^2] + m sqrt[a^2 + b^2 m^2])/(1 + m^2)):}`

but

#{(x^2=a^2/(1 + m^2)^2 + (2 b^2 m^2)/(1 + m^2)^2 + (a^2 m^4)/(1 + m^2)^2 - ( 2 m sqrt[b^2 + a^2 m^2] sqrt[a^2 + b^2 m^2])/(1 + m^2)^2),(y^2=b^2/(1 + m^2)^2 + (2 a^2 m^2)/(1 + m^2)^2 + (b^2 m^4)/(1 + m^2)^2 + ( 2 m sqrt[b^2 + a^2 m^2] sqrt[a^2 + b^2 m^2])/(1 + m^2)^2):}#

Now making `x^2+y^2` and simplifying we get

`x^2+y^2=a^2+b^2` which is a circle centered at the origin, with radius `sqrt(a^2+b^2)`