Transverse Common Tangent
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The equation of the common tangent to the circles x2 + y2 − 4x + 6y − 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 at their point of contact.
- 12x + 5y + 19 = 0
- 5x + 12y + 19=0
- 5x − 12y + 19 = 0
- 12x − 5y + 19 = 0
- y+2=16−3√237(x+1)
- y+2=16+3√237(x+1)
- y+1=x+3√2
- y+1=x−3√2
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
Only 1, 2, 3
Only 1, 2, 5
Only 1, 2, 3, 4
All 1, 2, 3, 4, 5
Find the equations of transverse common tangents for two circles
x2 + y2 + 6x − 2y + 1 =0 , x2 + y2 − 2x − 6y + 9 = 0
35x2 + 12xy − 18x = 0
35y2 + 12xy − 18y = 0
3x2 − 4xy + 16y − 12x = 0
3y2 − 4xy + 16x − 12y = 0
Let c1& c2 be the centers and r1& r2 be the radius of two circles. Then
Cases Conditions
p. 1.|r1−r2|< c1c2< r1+r2
q. 2. |r1−r2|=c1c2
r. 3.c1c2< |r1+r2|
s.
4. r1+r2< c1r2
t. 5. r1+r2=c1r2
p - 5, q - 4 , r - 1, s - 2 , t - 3
p - 4, q - 5 , r - 1, s - 3 , t - 2
p - 1, q - 2 , r - 3, s - 4 , t - 5
p - 4, q - 5 , r - 1 , s - 2 , t - 3
Find the Slope of the transverse common tangent to the circles x2 + y2 − 4x + 6y − 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0
−512
512
125
−125
- 15 units
- 18 units
- 20 units
- 24 units