Question

A) How many times does the line y = -6 intersect with the circle x² + y² = 36 ?

b) Hence, use a single word to describe what the line is to the circle.

Answer 1

• a) Once,
• b) Tangent.

Explanation:

Part A

General equation of circle:

• (x - h)² + (y - k)² = r², where (h, k) is center and r- radius

Comparing with the general equation we see that the circle x² + y² = 36 has:

• Center at the origin,
• Radius of 6 units.

The circle radius of 6 units, so y = - 6 has only one common point.

Part B

Since there is only one common point of the circle and line, the line is tangent to the circle.