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Grade: 11
        
The locus of the orthocentre of a triangle formed by the line (1+p)x-py+p(1+p)=0,(1+q)x-qy+q(1+q)=0,x=0 and p≠q is a straight line of slope is 
Please explain fully
5 days ago

Answers : (1)

Arun
15947 Points
							
 

Intersection point of y = 0 with first line is the point B(-p, 0)

        Intersection point of y = 0 with second line is the point A(-q, 0)

        Intersection point of the two lines is the point C(pq, (p + 1)(q + 1))

        Altitude from C to AB is x = pq

        Altitude from B to AC is y = -q/1+q (x + p)

        On solving these two we get x = pq and y = -pq

        => locus of orthocenter is x + y = 0.

5 days ago
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