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The ends of latus rectum of a parabola are (6,7),(6,-1). It`s vertex is???/

with solution

We know that length of Lattice rectum is 4a ( here "a" is the distance between focus and vertex ) so 4a = 8a=2(distance between focus and vertex) And from end points of Lattice rectum foci is centre of these two point So foci is(6,3)So vertex will be (4,3) since distance between focus and vertex is 2 units So equation of parabola is(Y-3)^2=4×2(x-4)(Y-3)^2=8(x-4)