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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
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
A.
π/3
We know that angle between two lines is 
l +m +n= 0
⇒ l = - (m+n)
⇒ (m+n)2 = l2
⇒ m2 +n2 +2mn = m2 +n2
[∵ l2 = m2 +n2, given]
⇒ 2mn = 0
when m = 0 ⇒ l =-n
Hence, (l, m, n) is (1,0-1)
When n =0, then l =-m
Hence, (l,m,n) is (1,0-1)
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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