The equation of an altitude of an equilateral triangle is and one of the vertices is 


The possible number of triangle is 


a) 
1 
b) 
2 
c) 
3 
d) 
4 
The equation of an altitude of an equilateral triangle is and one of the vertices is 


The possible number of triangle is 


a) 
1 
b) 
2 
c) 
3 
d) 
4 
(b)
Let the triangle be with and altitude drawn through vertex (meeting at ) be . If is , then we have
And coordinates of is . Let coordinates of vertex be . Then,
Hence, the remaining vertices are (0, 0) and or and . Also, the orthocenter is or (2, 0)
For points and of the coordinate plane, a new distance is defined by . Let and . Consider the set of points in the first quadrant which are equidistant (with respect to the new distance) from and 


The set of points consists of 


a) 
One straight line only 

b) 
Union of two line segments 

c) 
Union of two infinite rays 

d) 
Union of a line segment of finite length and an infinite ray 
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