Both circles are non-intersecting.

Hence there are four common tangents.

Transverse common tangents :

coordinate of P ≡

Let slope of these tangents is m

y – = m(x – 0) ⇒ mx – y + = 0

Now = 1 ⇒ =

⇒ m 2 + – m = 1 + m 2 ⇒ m = – , other tangents is vertical

Equation of tangents x = 0

– x – y + = 0 ⇒ –3x – 4y + 10 = 0 ⇒ 3x + 3y = 10

Direct common tangents

coordinate of Q ≡ Q(3, 4)

Hence equations y – 4 = m(x – 3) ⇒ mx – y + (4 – 3m) = 0

⇒ = 1 ⇒ |1 – 2m| = ⇒ 1 + 4m 2 – 4m = 1 + m 2 ⇒ 3m 2 – 4m = 0 ⇒ m = 0,

Hence equation y – 4 = 0(x – 3) ⇒ y = 4 ⇒ y – 4 = (x – 3) ⇒ 4x – 3y = 0

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