AP EAMCET · Maths · Ellipse
The equation of the normal drawn at the point \((\sqrt{2}+1,-1)\) to the ellipse \(x^2+2 y^2-2 x+8 y+5=0\) is
- A \(x+y=\sqrt{2}\)
- B \(x-2 y=3+\sqrt{2}\)
- C \(\sqrt{2} x-y=3+\sqrt{2}\)
- D \(2 x+y=2 \sqrt{2}+1\)
Answer & Solution
Correct Answer
(C) \(\sqrt{2} x-y=3+\sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(2x + 4y \frac{dy}{dx} - 2 + 8 \frac{dy}{dx} = 0\) \(\frac{dy}{dx} = \frac{2-2x}{4y+8} = \frac{1-x}{2y+4}\) \(m_{tangent} = \frac{1-(\sqrt{2}+1)}{2(-1)+4} = \frac{-\sqrt{2}}{2}\) \(m_{normal} = -\frac{1}{m_{tangent}} = -\frac{1}{-\frac{\sqrt{2}}{2}} = \sqrt{2}\)…
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