Question

Let A be a variable point on the line `y=4`, if 'B' and 'C' are variable points on the line `y=-4`, such that triangle ABC is an equilateral triangle, then the locus of the orthocentre of the triangle ABC is?

Answer 1

Vertex `A` of variable equilateral `DeltaABC` lies on line `y=4` and it's base `BC` lies on the line `y=-4`. So ordinate of `A` is `4` and ordinates of `BandC` are `-4`.
Since `DeltaABC` is equilateral its orthocenter `O` will coincide with centroid and the ordinate of orthocenter will always be `=1/3(4-4-4)=-4/3`

Hence locus of orthocenter centre will be `y=-4/3 or3y+4=0`