TS EAMCET · Maths · Ellipse
The equation of the ellipse with directrix \(3 x+4 y-5=0\), focus \((1,2)\) and eccentricity \(\frac{1}{2}\), is
- A \(x^2+84 y^2-24 x y-360 y+170 x+475=0\)
- B \(91 x^2+84 y^2-24 x y-170 x-360 y+475=0\)
- C \(91 x^2+84 y^2-24 x y-170 x+360 y+475=0\)
- D \(91 x^2+84 y^2-24 x y-170 x-360 y-475=0\)
Answer & Solution
Correct Answer
(B) \(91 x^2+84 y^2-24 x y-170 x-360 y+475=0\)
Step-by-step Solution
Detailed explanation
The equation of ellipse with directrix \(3 x+4 y-5=0\), focus \((1,2)\) and eccentricity \(\frac{1}{2}\), by definition, we have \(\sqrt{(x-1)^2+(y-2)^2}=\frac{1}{2} \frac{(3 x+4 y-5)}{5}\) \(\Rightarrow \quad 100\left[x^2+y^2-2 x-4 y+5\right]=(3 x+4 y-5)^2\)…
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