Answer:
a) The line intersects with the circle once.
b) Tangent
Step-by-step explanation:
We are given the following equation for the circle:
[tex]x^2 + y^2 = 36[/tex]
How many times does the line y=-6 intersect with the circle?
We have to find the values of x when [tex]y = -6[/tex]
So
[tex]x^2 + y^2 = 36[/tex]
[tex]x^2 + (-6)^2 = 36[/tex]
[tex]x^2 + 36 = 36[/tex]
[tex]x^2 = 0[/tex]
[tex]x = 0[/tex]
Since the line intersects the circle at one point, it is tangent to the circle.
The line intersects with the circle once.
