Number of direct common tangents to circles x^2 + y^2 = 4 and x^2 + y^2 -8x -8y + 7 = 0 , is

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10-1.Circle and System of Circles

normal

The number of direct common tangents to the circles $x^2 + y^2 = 4$ and $x^2 + y^2 -8x -8y + 7 = 0$ , is

A

$0$

B

$1$

C

$2$

D

$3$

Solution

$\mathrm{C}_{1}(0,0)$ and $\mathrm{r}_{1}=2$

Also, $C_{2}(4,4)$ and $r_{2}=5$

Since, $c_{1} c_{2}=4 \sqrt{2}$

$\Rightarrow \quad\left|\mathrm{r}_{1}-\mathrm{r}_{2}\right|<\mathrm{c}_{1} \mathrm{c}_{2}<\mathrm{r}_{1}+\mathrm{r}_{2}$

$\Rightarrow$ Circles are intersecting.

$\Rightarrow$ Two direct common tangents exist.

Standard 11

Mathematics

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