Question

If the circles x² + y² = a and x² + y² – 6x – 8y + 9 = 0, touch externally, then a =

A. 1

B. - 1

C. 21

D. 16

Answer 1

Correct option is A. 1

Given that the circles x² + y² = a and x² + y² - 6x - 8y + 9 = 0 touch each other externally.

We need to find the value of a.

We know that if the circles touch each other externally, the distance between the centres is equal to the sum of the radii of two circles.

We know that for a circle x² + y² + 2ax + 2by + c = 0

⇒ Centre = (- a, - b)

⇒ Radius = \(\sqrt{a^2+b^2-c}\)

For x² + y² = a

⇒ Centre(C₁) = (0,0)

⇒ Radius(r₁) = \(\sqrt{0+0-(-a)}\)

⇒ r₁ = √a

For x² + y² - 6x - 8y + 9 = 0

We have C₁C₂ = r₁ + r₂