Question

Show that the curve x y equal to a square and x square + y square equal to 2 a square touch each other

Answer 1

Answer:

Step-by-step explanation:

x^2+y^2 +2xy=2a^+2a^2= 4a^2  

(x+y)^2 =(2a)^2  

Therefore x+y =2a.........(i)  

and xy = a^2 .............(ii)  

(x-y)^2 =(x+y)^2 -4xy  

(x-y)^2 =4a^2 -4a^2 =0  

x-y =0 or x =y  

from (ii)  

(x)(x) =a^2 or x =a and y =a ....(iii)  

since the solution is only one therefore they are touching....................Ans