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Multiple Choice QuestionsThe number of common tangent to the circles x2+y2-4x-6y-12=0 and x2+y2+6x+18y+26 = 0 is
1
2
3
3
C.
3
Number of common tangents depend on the position of the circle with respect to the each other.
(i) If circles touch externally ⇒C1C2 = r1+ r2,3 common tangents
(ii) If circles touch internally ⇒ C1C2 = r2-r1, 1 common tangents
(iii) If circles do not touch each other, 4 common tangents
Given equations of circles are
x2 +y2-4x-6y-12 = 0 .. (i)
x2+y2+6x+18y+26 =0 ... (ii)
Centre of circle (i) is C1 (2,3) and radius
=
Centre of circle (ii) is C2(-3,-9) and radius
Thus, both circles touch each other externally. Hence, there are three common tangents.
The angle between the lines whose direction cosines satisfy the equations l +m+n=0 and l2 = m2+n2 is
π/3
π/4
π/6
π/6
If PS is the median of the triangle with vertices P(2,1), Q(6,-1) and R (7,3), then equation of the line passing through (1,-1) and parallel to PS is
4x-7y - 11 =0
2x+9y+7=0
4x+7y+3 = 0
4x+7y+3 = 0
Let a,b,c and d be non-zero numbers. If the point of intersection of the lines 4ax +2ay +c= 0 and 5bx +2by +d = 0 lies in the fourth quadrant and is equidistant from the two axes, then
2bc-3ad =0
2bc+3ad =0
2ad-3bc =0
2ad-3bc =0
are the vertices of triangle ABC, then prove that its centroid G is 
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