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TS EAMCET · Maths · Ellipse

Equation of a common tangent to the circle \(x^2+y^2=4\) and to the ellipse \(2 x^2+25 y^2=50\) is

  1. A \(\sqrt{2} x+\sqrt{21} y+\sqrt{23}=0\)
  2. B \(\sqrt{2} x-\sqrt{21} y+2 \sqrt{23}=0\)
  3. C \(\sqrt{19} x-\sqrt{2} y+2 \sqrt{21}=0\)
  4. D \(\sqrt{19} x-y+2 \sqrt{20}=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\sqrt{2} x-\sqrt{21} y+2 \sqrt{23}=0\)

Step-by-step Solution

Detailed explanation

Let \(y=m x+c\) is common tangent of circle \(x^2+y^2=4\) and ellipse \(\frac{x^2}{25}+\frac{y^2}{2}=1\) \(\therefore \quad y=m x \pm 2 \sqrt{1+m^2}\) and \(y=m x \pm \sqrt{25 m^2+2}\) are coincide…