Transverse Common Tangent

Q.

Find the Slope of the transverse common tangent to the circles $x^2+y^2-4x+6y-12=0$ and $x^2+y^2+6x+18y+26=0$

1. 

2. 

3. 

4. 

Q.

With respect to position of two circles which of the following statements is/are correct?

1. If one circle lies completely outside the other circle,

Number of direct common tangents = 2

Number of transverse common tangents = 2

2. If two circles touch each other externally

Number of direct common tangents = 2

Number of transverse common tangents = 1

3. If two circles touch each other internally

Number of direct common tangents = 1

Number of transverse common tangents = 0

4. If two circles intersect each other at two points

Number of direct common tangents = 2

Number of transverse common tangents = 0

5. If one circle lies completely inside the other circle

Number of direct common tangents = 0

Number of transverse common tangents = 0

1. All 1, 2, 3, 4, 5

2. Only 1, 2, 3

3. Only 1, 2, 5

4. Only 1, 2, 3, 4