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Question

Find the equation of the parabola the extremities of whose latus rectum are (1,2) and (1,4).

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Solution

Let A and B be the endpoint of latus rectum of given parabole
respectively.
AB=6 unit
We know focuses is midpoint of latus rectum.Then coordinates of focus s=(1,1)
y=1 is axis of parabola and x=2 is tangent at vertex.
Equation of parabola [(y(1))2=4×a(x(2))]
=(y+1)2=4×3(x+2)
=(y+1)2=12(x+2)

1052324_712341_ans_0a8bf64bb4e6455cab28b987ebf771e8.png

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