Given equation is:

⇒ x² + y² + 2x - 4y + 5 = 0

We know that for a pair of straight lines ax² + 2hxy + by² + 2gx + 2fy + c = 0, the conditions to be satisfied is abc + 2fgh - af² - bg² - cf² = 0, h²≥ab, g²≥ca and f²≥bc.

Here we can see that h = 0 a = b = 1

⇒ h² = 0² = 0

⇒ ab = 1.1 = 1

⇒ h²≤ab. So, the equation doesn’t represent a pair of straight lines.

⇒ x² + y² + 2x - 4y + 5 = 0

⇒ (x² + 2x + 1) + (y² - 4y + 4) = 0

⇒ (x + 1)² + (y - 2)² = 0

The equation represents circle with zero radius. This is a point circle.

∴The correct option is (a).