Question

Sketch the circle given by x²+y²=1 and the line given by y=2x+2 on the same set of axes. One solution to the pair of equations is easily identifiable from the sketch. What is it?

Answer 1

(-0.6, 0.8) and (-1,0)

Explanation:

`x^2+y^2=1`

`y=2x+2`

Applying y value to the first equation

`x^2+(2x+2)^2=1\\\Rightarrow x^2+4x^2+4+8x=1\\\Rightarrow 5x^2+8x+3=0`

Solving the equation

`x=(-8+√(8^2-4\cdot \:5\cdot \:3))/(2\cdot \:5), (-8-√(8^2-4\cdot \:5\cdot \:3))/(2\cdot \:5)\\\Rightarrow x=-0.6, -1`

When x = -0.6

`y=2* -0.6+2\\\Rightarrow y=0.8`

When x = -1

`y=2* -1+2\\\Rightarrow y=0`

So, the points where the circle and line will intersect are (-0.6, 0.8) and (-1,0)