Question

I NEEDD HELPPPP PLSSSS SOME1 )):

Answer 1

The point is
`((3)/(5)√(5),(6)/(5)√(5))`

Explanation:

∵ The circle has center (0 , 0) and radius 3

∵ The equation of any circle is
`(x-h)^(2)+(y-k)^(2)=r^(2)`

where (h , k) is the center of the circle and r is the radius of it

∴
`x^(2)+y^(2)=3^(2)`

∴
`x^(2)+y^(2)=9`

∵ The equation of the line is y = 2x

We will substitute y in the equation of the circle by 2x

∴
`x^(2)+(2x)^(2)=9`

∴
`x^(2)+4x^(2)=9`

∴
`x^(2)=(9)/(5)`

∴
`x=\sqrt{(9)/(5)}=(3)/(√(5))((√(5))/(√(5)))=(3)/(5)√(5)`

∴ y =
`2((3)/(5)√(5))=(6)/(5)√(5)`

The line intersects the circle at point
`((3)/(5)√(5),(6)/(5)√(5))`

The decimal values (1.342 , 2.684)