Question

The circles x² + y² + 6x + 6y = 0 and x² + y² – 12x –12y = 0

Options

• cut orthogonally

• touch each other internally

• intersect two points

• touch each other externally

Answer 1

touch each other externally

Explanation:

The centres of given circles are C₁(–3, –3), C₂(6, 6) and radii are

r₁ = `sqrt(9 + 9 + 0) = 3sqrt(2)`, r₂ = `sqrt(36 + 36 + 0) = 6sqrt(2)`, respectively.

Now, C₁C₂ = `sqrt((6 + 3)^2 + (6 + 3)^2)`

= `9sqrt(2)`

and r₁ + r₂ = `3sqrt(2) + 6sqrt(2)`

= `9sqrt(2)`

Here, C₁C₂ = r₁ + r₂

So, both circles touch each other externally.