Question

The number of common tangents to the circles x² + y² - x = 0 and x² + y² + x = 0 is ______ 

Options

• 2

• 1

• 4

• 3

Answer 1

The number of common tangents to the circles x² + y² - x = 0 and x² + y² + x = 0 is 3.

Explanation:

The centres and radii of the circles are Centres: 

`C_1(1/2, 0), C_2(-1/2, 0)`

Radii : `r_1 = 1/2 r_2 = 1/2`

Clearly, C₁C₂ = r₁ + r₂. Therefore, the circles touch each other externally. Hence, there are 3 common tangents.