JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If \(x^{2}+9 y^{2}-4 x+3=0, x, y \in R\), then \(x\) and \(y\) respectively lie in the intervals:
- A \(\left[-\frac{1}{3}, \frac{1}{3}\right]\) and \(\left[-\frac{1}{3}, \frac{1}{3}\right]\)
- B \(\left[-\frac{1}{3}, \frac{1}{3}\right]\) and \([1,3]\)
- C \([1,3]\) and \([1,3]\)
- D \([1,3]\) and \(\left[-\frac{1}{3}, \frac{1}{3}\right]\)
Answer & Solution
Correct Answer
(D) \([1,3]\) and \(\left[-\frac{1}{3}, \frac{1}{3}\right]\)
Step-by-step Solution
Detailed explanation
\(x^{2}+9 y^{2}-4 x+3=0\) \(\left(x^{2}-4 x\right)+\left(9 y^{2}\right)+3=0\) \(\left(x^{2}-4 x+4\right)+\left(9 y^{2}\right)+3-4=0\) \((x-2)^{2}+(3 y)^{2}=1\) \(\frac{(x-2)^{2}}{(1)^{2}}+\frac{y^{2}}{\left(\frac{1}{3}\right)^{2}}=1\) (equation of an ellipse). As it is equation…
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