TS EAMCET · Maths · Ellipse
If origin is the centre, \(X\)-axis is the major axis and \(\sqrt{\frac{2}{5}}\) is the eccentricity of an ellipse which passes through \((-3,1)\), then the equation of that ellipse is
- A \(3 x^2+5 y^2=32\)
- B \(2 x^2+y^2=19\)
- C \(x^2+23 y^2=32\)
- D \(x^2+2 y^2=11\)
Answer & Solution
Correct Answer
(A) \(3 x^2+5 y^2=32\)
Step-by-step Solution
Detailed explanation
Given, the major axis of the ellipse lies on the \(X\)-axis, so it equation is \[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \quad\left(a^2>b^2\right) \] Since, it is passes through \((-3,1)\) \[ \therefore \quad \frac{9}{a^2}+\frac{1}{b^2}=1 \] And also, \(b^2=a^2\left(1-e^2\right)\)…
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