Question

Draw a graph of the circle with equation x²+y²=9.What are the solutions to the system of circle and line when the circle is given by x²+y²=9, and the line is given by y=2?

Answer 1

(-2.23606, 2) and (2.23606, 2)

Explanation:

`x^2+y^2=9`

`y=2`

The circle has its center situated at the origin and radius of 3 units

Applying the value of y to the first equation

`x^2+2^2=9`

`\Rightarrow x^2=9-4`

`\Rightarrow x^2=5`

`\Rightarrow x=√(5)`

`\Rightarrow x=\pm 2.23606`

So, the points where the line will intersect the circle is (-2.23606, 2) and (2.23606, 2)