Question

Number of intersection points of the curves x2 + y2 = 9 and 2xy = 2, is

Answer 1

Answer:

we have,

    x^2+y^2=9    

[this is a equation of circle with center 0,0 and radius 3]

so equation becomes,

        x^2+y^2=3^2  =>>  x + y =3      .......(1)

    2xy = 2   . ...............(2)

Step-by-step explanation:

hence,

         from (2) ,we get

            x = 2/2y   =>>  1/y    ............(3)

putting 3 in 1 we get,

            1/y+y=3  =>> 1 + y^2 =3y  >>  y^2-3y+1=0

  >>  x= 3 /2 + 1 /2 √5 or x= 3 /2 -1 /2 √5

hence putting values of x in eq 3 we got the values of y

and hence for every value of x the corresponding value of y be the point of intersection of these curves.

I hope it helps.

Answer 2

    x^2+y^2=9    

[this is a equation of circle with center 0,0 and radius 3]

so equation becomes,

        x^2+y^2=3^2  =>>  x + y =3      .......(1)

    2xy = 2   . ...............(2)

Step-by-step explanation:

hence,

         from (2) ,we get

            x = 2/2y   =>>  1/y    ............(3)

putting 3 in 1 we get,

            1/y+y=3  =>> 1 + y^2 =3y  >>  y^2-3y+1=0

  >>  x=

3

/2

+

1

/2

√5 or x=

3

/2

-1

/2

√5

hence putting values of x in eq 3 we got the values of y

and hence for every value of x the corresponding value of y be the point of intersection of these curves.