Question

I NEED HELP PLSSSS SOMEONE DD:

Answer 1

Answer:

The point of intersection is (4.472 , 3.236)

Step-by-step 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

∴ $x^{2}+(0.5x+1-1)^{2}=25$

∴ $x^{2}+(0.5x)^{2}=25$

∴ $x^{2}+0.25x^{2}=25$

∴ $1.25x^{2}=25$

∴ $x^{2}=\frac{25}{1.25}=20$

∴ x=$\sqrt{20}=4.472$

∴ y = 0.5(4.472) + 1 = 3.236

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