ParabolaMedium
Question
If x + y = k is normal to y2 =12x , then k is
Options
A.3
B.9
C.-9
D.-3
Solution
If y = mx + c is normal to the parabola y2 = 4ax , then c = -2am - am3
From given condition, y2 = 12 x
⇒ y2 = 4.3.x ⇒ a = 3
And x + y = k
⇒ y = (-1)x + k ⇒ m = - 1
and c = k
∴ c = k = -2(3)(-1) - 3(-1)3 = 9
From given condition, y2 = 12 x
⇒ y2 = 4.3.x ⇒ a = 3
And x + y = k
⇒ y = (-1)x + k ⇒ m = - 1
and c = k
∴ c = k = -2(3)(-1) - 3(-1)3 = 9
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