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Question

The latus rectum of the parabola whose directrix is x + y – 2 = 0 and the focus is (3, –4), is __________.

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Solution

For a given parabola
vertex is given by (0, 0), focus is (3, 4) and directrix is x + y − 2 = 0
Distance between directrix and focus is 2a

i.e. 3-4-21+1 = 2ai.e. 32 = 2ai.e. a = 322
Length of latus rectum is 4a=4×322=2×32=32 =32

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