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Show that the locus of the orthocenter of the triangles formed by the lines (1+p)x-py+p(1+p)=0, (1+q)x-qy+q(1+q)=0 and y=0 is a straight line. |
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Answer» 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. |
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