TS EAMCET · Maths · Ellipse
One of the foci of an ellipse is \((2,-3)\) and its corresponding directrix is \(2 x+y=5\). If the eccentricity of the ellipse is \(\frac{\sqrt{5}}{3}\) then the coordinates of the other focus are
- A \((18,5)\)
- B \((4,-2)\)
- C \((-2,-5)\)
- D \((-4,-6)\)
Answer & Solution
Correct Answer
(C) \((-2,-5)\)
Step-by-step Solution
Detailed explanation
\(d = \frac{|2(2)+(-3)-5|}{\sqrt{2^2+1^2}} = \frac{|-4|}{\sqrt{5}} = \frac{4}{\sqrt{5}}\) \(d = a(\frac{1}{e}-e) \implies \frac{4}{\sqrt{5}} = a(\frac{3}{\sqrt{5}}-\frac{\sqrt{5}}{3}) = a(\frac{9-5}{3\sqrt{5}}) = a(\frac{4}{3\sqrt{5}}) \implies a = 3\)…
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