Question

the latus rectum of a parabola had endpoints (-2,3) and (6,3). find two possible equations

Answer 1

since the ends of the latus rectum is (-2,3) and (6,3) thus focus is at midpoint of (-2,3) and (6,3) and co-ordinates of focus is (2,3)

Answer 2

since length of latus rectum is (6-(-2))=8 units [(8/4=2)]
vertex of the parabola is at either (2,1) or (2,5)

Answer 3

thus the eq of parabola is a) (x-2)^2=8(y-1) (openning upward)

Answer 4

b) a) (x-2)^2=-8(y-5) (opeening downward)

Answer 5

its better to draw the graph