Question

How many times does the line y=-6 intersect with the circle x^2+y^2=36?

Answer 1

a) The line intersects with the circle once.

b) Tangent

Explanation:

We are given the following equation for the circle:

`x^2 + y^2 = 36`

How many times does the line y=-6 intersect with the circle?

We have to find the values of x when
`y = -6`

So

`x^2 + y^2 = 36`

`x^2 + (-6)^2 = 36`

`x^2 + 36 = 36`

`x^2 = 0`

`x = 0`

Since the line intersects the circle at one point, it is tangent to the circle.

The line intersects with the circle once.