Question

The number of common tangents to the circles $ {{x}^{2}}+{{y}^{2}}=4 $ and $ {{x}^{2}}+{{y}^{2}}-8x+12=0 $ is:

• A. 1
• B. 2
• C. 3
• D. 4
• E. none of these

Answer 1

Answer: (C)

The centre and radius of circle $ {{x}^{2}}+{{y}^{2}}=4 $ are $ {{C}_{1}}(0,\text{ }0) $ and $ {{r}_{1}}=2 $ respectively and the centre and radius of circle $ {{x}^{2}}+{{y}^{2}}-8x+12=0 $ are $ (4,0) $ and $ {{r}_{2}}=2 $ . $ \because $ $ {{C}_{1}}{{C}_{2}}={{r}_{1}}+{{r}_{2}} $ $ \therefore $ Circles touch each other externally, therefore number of common tangents are 3.