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TS EAMCET · Maths · Ellipse

If a normal is drawn at a variable point \(\mathrm{P}(x, y)\) on the curve \(9 x^2+16 y^2-144=0\), then the maximum distance from the centre of the curve to the normal is

  1. A \(1\)
  2. B \(7\)
  3. C \(12\)
  4. D \(\frac{3}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(1\)

Step-by-step Solution

Detailed explanation

Curve: \( \frac{x^2}{16} + \frac{y^2}{9} = 1 \). Center \((0,0)\). \(a=4, b=3\). Equation of normal at \( \mathrm{P}(4\cos\theta, 3\sin\theta) \): \( 4x\sec\theta - 3y\csc\theta = 4^2 - 3^2 = 7 \). Distance \(d\) from \((0,0)\) to normal:…