AP EAMCET · Maths · Ellipse
Foci of the ellipse \(2 x^2+3 y^2-4 x-12 y+13=0\) are
- A \(\left(1+\frac{1}{\sqrt{6}}, 2\right)\) and \(\left(1-\frac{1}{\sqrt{6}}, 2\right)\)
- B \(\left(\frac{1}{\sqrt{6}}+1,2\right)\) and \(\left(\frac{1}{\sqrt{6}}-1,2\right)\)
- C \(\left(2,1+\frac{1}{\sqrt{6}}\right)\) and \(\left(2,1-\frac{1}{\sqrt{6}}\right)\)
- D \(\left(2, \frac{1}{\sqrt{6}}+1\right)\) and \(\left(2, \frac{1}{\sqrt{6}}-1\right)\)
Answer & Solution
Correct Answer
(A) \(\left(1+\frac{1}{\sqrt{6}}, 2\right)\) and \(\left(1-\frac{1}{\sqrt{6}}, 2\right)\)
Step-by-step Solution
Detailed explanation
Given ellipse \(\begin{array}{rlrl} & & 2 x^2+3 y^2-4 x-12 y+13 & =0 \\ \Rightarrow & 2(x-1)^2+3(y-2)^2 & =1 \\ \Rightarrow & & \frac{(x-1)^2}{\left(\frac{1}{\sqrt{2}}\right)^2}+\frac{(y-2)^2}{\left(\frac{1}{\sqrt{3}}\right)^2} & =1 \end{array}\)…
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