Answer:
Yes, they will intercept.
The circle, y² + x² = 64, intersects with g(x) at the points (8,0) and (-4.8,-6.4)
Step-by-step explanation:
x g(x)
−1 −4.5
0 −4
1 −3.5
y2 + x2 = 64
First of, we find the equation for g(x).
It is stated that g(x) is a linear function, hence, it has the equation of straight line.
y = mx + c [where y = g(x), m = slope, c = y-intercept]
Putting the values of x and corresponding y into the equation of a straight line, we can obtain the equation of the straight line.
x y
−1 −4.5
0 −4
1 −3.5
-4.5 = -m + c (from the first line)
-4 = c (from the second line)
-3.5 = m + c (from the third line)
So, from these relation, it is evident that
c = -4, m = 0.5
g(x) = y = 0.5x - 4
The equation of the circle is
y² + x² = 64
If the circle and the line, g(x), are to intersect, they will have the same coordinates At the point of intersection.
Equation of line
y = 0.5x - 4
Substituting this value for y in the equation of the circle
y² + x² = 64
(0.5x - 4)² + x² = 64
0.25x² - 4x + 16 + x² = 64
1.25x² - 4x - 48 = 0
Solvingthe quadratic equation
x = 8 or x = - 4.8
when x = 8, y = 0.5(8) - 4 = 0
when x = 4.8, y = 0.5(-4.8) - 4 = -6.4
therefore, it is evident that the circle, y² + x² = 64, intersects with g(x) At the points (8,0) and (-4.8,-6.4)
Hope this Helps!!+
