TS EAMCET · Maths · Ellipse
The longest distance of the point \((a, 0)\) from the curve \(2 x^2+y^2=2 x\) is
- A \(1+a\)
- B \(|1-a|\)
- C \(\sqrt{1-2 a+2 a^2}\)
- D \(\sqrt{1-2 a+3 a^2}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{1-2 a+2 a^2}\)
Step-by-step Solution
Detailed explanation
Given, curve is \(2 x^2+y^2=2 x\) \(2 x^2-2 x+y^2=0\) \(\Rightarrow \quad 2\left(x-\frac{1}{2}\right)^2+y^2=\frac{1}{2}\) \(\Rightarrow \quad \frac{\left(x-\frac{1}{2}\right)^2}{\frac{1}{4}}+\frac{y^2}{\frac{1}{2}}=1\) which represents an ellipse. Here,…
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