Answer: Option C
:
C
To find the no. of common tangents, let's find the relation betweendistance between the centers of these circles and sum of their radii -
Co-ordiantes of thecenter of first circle is (-1, - 4)
Co-ordiantes of thecenter of second circle is (2, 5)
thus the distance between them is - $\sqrt{(3^2+9^2)}$
= 3$\sqrt{(}10)$
Now, the sumtheir radii will be -
Radius of the first circle is - 2$\sqrt{(}10)$
Radius of the secondcircle is-$\sqrt{(}10)$
Sum of them will be -3$\sqrt{(}10)$
Since, the distance between the centres is equal to sum of their radii
Number of common tangents will be3.