Transverse Common Tangent

Q.

Let $c_1\&c_2$ be the centers and $r_1\&r_2$ be the radius of two circles. Then

Cases Conditions

p. 1.$|r_1-r_2|<c_1{c}_2<r_1+r_2$

q. 2. $|r_1-r_2|=c_1{c}_2$

r. 3.$c_1{c}_2<|r_1+r_2|$

s.

4. $r_1+r_2<c_1{r}_2$

t. 5. $r_1+r_2=c_1{r}_2$

1. p - 5, q - 4 , r - 1, s - 2 , t - 3

2. p - 1, q - 2 , r - 3, s - 4 , t - 5

3. p - 4, q - 5 , r - 1, s - 3 , t - 2

4. p - 4, q - 5 , r - 1 , s - 2 , t - 3

Q.

Find the equations of transverse common tangents for two circles

$x^2+y^2+6x-2y+1=0,x^2+y^2-2x-6y+9=0$

1. $35x^2+12xy-18x=0$

2. $35y^2+12xy-18y=0$

3. $3x^2-4xy+16y-12x=0$

4. $3y^2-4xy+16x-12y=0$

Q. Find the radius of the circle passing through the point (-6, 8) centered at the origin.

1. 8 units
2. 9 units
3. 10 units
4. 12 units