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A curve passes through (-2, 0) and has, at every point, a sub-normal of constant length 4 units. Which of the following statements are correct? (A) There are two possible parabolas which touch each other. (B) The area bounded by a possible curve and the y-axis is 32/3. (C) There is a unique such curve. (D) The line x + 2 = 0 is tangent to the curve.
- (A) and (B)
- (C) only
- (B) and (C)
- (A) and (D)
Correct answer: (A) and (B)
Solution
The constant sub-normal condition gives y² = 8(x+2) and y² = -8(x+2); both pass through (-2,0) and touch there, and each encloses area 32/3 with the y-axis. So (A) and (B) hold, not (C) or (D).
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