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AP EAMCET · Maths · Ellipse

The equations of the tangents to the ellipse \(9 x^2+16 y^2=144\) which pass through the point \((2,3)\) are

  1. A \(x+y=5, y=3\)
  2. B \(x+y+5=0, y=3\)
  3. C \(x+y=5, y+3=0\)
  4. D \(x+y+5=0, y+3=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x+y=5, y=3\)

Step-by-step Solution

Detailed explanation

\( \frac{x^2}{16} + \frac{y^2}{9} = 1 \) \( y = m x \pm \sqrt{16 m^2 + 9} \) \( 3 = 2m \pm \sqrt{16 m^2 + 9} \) \( (3 - 2m)^2 = 16 m^2 + 9 \) \( 9 - 12m + 4m^2 = 16 m^2 + 9 \) \( 12m^2 + 12m = 0 \) \( 12m(m+1) = 0 \) \( m = 0 \text{ or } m = -1 \) For \( m=0 \):…