Question

I NEED HELP PLSSSS SOMEONE DD:

Answer 1

The point of intersection is (4.472 , 3.236)

Explanation:

∵ The center of the circle is (0 , 1) and its radius = 5

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

∴
`(x-0)^(2)+(y-1)^(2)=5^(2)`

∴
`x^(2)+(y-1)^(2)=25`

∵ The equation of the line which intersects the circle is y = 0.5x + 1

By substitute y in the equation of the circle by 0.5x + 1

∴
`x^(2)+(0.5x+1-1)^(2)=25`

∴
`x^(2)+(0.5x)^(2)=25`

∴
`x^(2)+0.25x^(2)=25`

∴
`1.25x^(2)=25`

∴
`x^(2)=(25)/(1.25)=20`

∴ x=
`√(20)=4.472`

∴ y = 0.5(4.472) + 1 = 3.236

∴ The line intersects the circle at point (4.472 , 3.236)