A normal is drawn at a point P(x, y) of a curve. If meets the x-axis at Q. If PQ is of constant length k, and the curve passes through (0, k), then the equation of the curve is
A normal is drawn at a point P(x, y) of a curve. If meets the x-axis at Q. If PQ is of constant length k, and the curve passes through (0, k), then the equation of the curve is
Option 1 -
x² + y² = k²
Option 2 -
x² – y² = k²
Option 3 -
x² + y² = k² - 1
Option 4 -
x² – y² = k² – 1
Asked by Shiksha User
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1 Answer
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Correct Option - 1
Detailed Solution:Length of normal
k = y √ (1 + (dy/dx)²)⇒ ∫ (y dy) / √ (k² - y²) = ∫ dx
Let k² – y² = t²
-2y dy = 2t dt
-√ (k² - y²) = x + c
It passes through (0, k)
x² + y² = k²
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