If the line y = - 7 2 is the directrix of the parabola x 2 - k y + 8 = 0 , then the sum of all the possible values of k is equal to

Question

If the line y = - 7 2 is the directrix of the parabola x 2 - k y + 8 = 0 , then the sum of all the possible values of k is equal to,

MARKS App · Accepted Answer

Given equation of the parabola is x 2 - k y + 8 = 0 ⇒ x 2 = k y - 8 k ⇒ Directrix is y = 8 k - k 4 ⇒ y = - 7 2 is same as y = 8 k - k 4 ⇒ 32 - k 2 4 k = - 7 2 ⇒ - k 2 + 14 k + 32 = 0 ⇒ k 1 + k 2 = 14 (sum of possible values of k )

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