Question

Trevor is analyzing a circle, y2 + x2 = 49, and a linear function g(x). Will they intersect?

Answer 1

they will not intersect i just took the test.

Explanation:

Answer 2

We have a circumference that is given by the following equation:


`x^(2)+y^(2)=49`

We can write this equation in its standard form as follows:


`x^(2)+y^(2)=7^(2) \\ where \ the \ radius \ r=7`

On the other hand, the linear function is given as the following table:


`x \ \ \ \ \ \ \ \ g(x) \\ -1 \ \ -9.2 \\ 0 \ \ \ \ \ -9 \\ 1 \ \ \ \ \ -8.8`

To check if the circle and the line intersects, let's substitute the equation of the line into the equation of the circle to see if there is a real solution, so:


`x^(2)+(0.2x-9)^(2)=49 \\ \\ \therefore x^(2)+0.04x^(2)-3.6x+81=49 \\ \\ \therefore 1.04x^(2)-36x+32=0 \\ \\ Solving \ for \ x: \\ x_(1)=33.70 \\ x_(2)=0.91 \\ \\ Solving \ for \ y: \\ y_(1)=0.2(33.70)-9=-2.26 \\ y_(2)=0.2(0.91)-9=-8.18`

Finally the intersects are:


`P_(1)(33.70, -2.26) \ and \ P_(2)(0.91, -8.18)`