Question

Ally is analyzing a circle, y2 + x2 = 4, and a linear function g(x). Will they intersect?

Answer 1

The linear function gives us the points
(0,3)
(4,0)
(8,-3)

find the equation
hm
find slope
(y2-y1)/(x2-x1)
for (0,3) and (4,0)
slope=(0-3)/(4-0)=-3/4

y=-3/4x+b
given
(0,3)
y=-3/4x+3


so sub -3/4x+3 for y in other equation
(-3/4x+3)^2+x^2=4
expand
9/2x^2-9/2x+9+x^2=4
11/2x^2-9/2x+9=4
times 2 both sides
11x^2-9x+18=8
minus 8 both sides
11x^2-9x+10=0
factor
or use quadratic formula
for
ax^2+bx+c=0
x=$\frac{-b+/- \sqrt{b^2-4ac} }{2a}$

11x^2-9x+10=0
x=$\frac{-(-9)+/- \sqrt{(-9)^2-4(11)(10)} }{2(11)}$
x=$\frac{9+/- \sqrt{81-440} }{22}$
x=$\frac{9+/- \sqrt{-359} }{22}$
we see we have no real roots
there are no intersection points

Answer 2

No they do not intercept at all

Hope this helps