2000
JEE Main 2000 Mathematics question on Conic Sections
If
x+y=k is normal to
y2=12x, then
k is
- A.
3
- B.
9
- C.
- D.
Show answer and solution
Correct option: B
Solution
For y² = 12x, we have 4a = 12, so a = 3. The normal at point (at², 2at) = (3t², 6t) has slope -t.
The line x + y = k has slope -1, so t = 1.
The point of contact is (3·1, 6·1) = (3, 6).
Substituting into x + y = k: k = 3 + 6 = 9.
[2000]
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