TS EAMCET · Maths · Circle
An ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) with eccentricity \(\frac{2 \sqrt{2}}{3}\) is inscribed in a circle \(x^2+y^2=18\) such that the length of its major axis is equal to the diameter of this circle. The locus of the poles of all the tangents of the circle with respect to the ellipse is
- A \(x^2+y^2=\frac{8}{9}\)
- B \(18 x+\frac{2 y}{9}=1\)
- C \(\frac{x^2}{18}+\frac{y^2}{9}=1\)
- D \(\frac{x^2}{18}+\frac{9 y^2}{2}=1\)
Answer & Solution
Correct Answer
(D) \(\frac{x^2}{18}+\frac{9 y^2}{2}=1\)
Step-by-step Solution
Detailed explanation
Equation of ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) \(e=\frac{2 \sqrt{2}}{3}\) Length of major axis is the diameter of circle \(x^2+y^2=18\) \(\therefore \quad 2 a=2(3 \sqrt{2})^2 \Rightarrow a=3 \sqrt{2}\) \(e^2=1-\frac{b^2}{a^2}\)…
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