Question

At which point does the line y = 2 - x intersect the circle (x - 3)2 + y2 = 25?

Answer 1

first write both the graphs in form P(x)=0

Answer 2

sorry, solve both of them for y

Answer 3

y=2-x

\[y^2=25-(x-3)^2\]
\[y=\pm \sqrt{25-(x-3)^2}\]

Answer 4

\[2-x=\pm \sqrt{25-(x-3)^2}\]

Answer 5

write this equation as two:
\[2-x=\sqrt{25-(x-3)^2}\] and \[2-x=-\sqrt{25-(x-3)^2}\]

Answer 6

solve each of them as usual

Answer 7

\[(2-x)^2=25-(x-3)^2\]
\[4-4x+x^2=25-x^2+6x-9\]

Answer 8

\[2x^2-10x-12=0\]
\[x^2-5x-6=0\]
\[(x-6)(x+1)=0\]
\[x={6, -1}\]

Answer 9

do the same hing with second equation and check for extraneous solutions

Answer 10

I got 3,4