SATHEE: Ellipse 1 Question 1

Ellipse 1 Question 1

1. An ellipse, with foci at $(0, 2)$ and $(0, - 2)$ and minor axis of length 4, passes through which of the following points?

(2019 Main, 12 April II)

(a) $(\sqrt{2}, 2)$

(b) $(2, \sqrt{2})$

(d) $(1, 2 \sqrt{2})$

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Answer:

Correct Answer: 1. (a)

Solution:

Let the equation of ellipse be

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

Since, foci are at $(0, 2)$ and $(0, - 2)$ , major axis is along the $Y$ -axis.

$So, b e = 2$

[where $e$ is the eccentricity of ellipse] and $2 a =$ length of minor axis $= 4$

[given]

$\begin{array}{ll} \Rightarrow & a = 2 \\ ∵ & e^{2} = 1 - \frac{a^{2}}{b^{2}} \\ ∴ & {\frac{2}{b}}^{2} = 1 - \frac{4}{b^{2}} \\ \Rightarrow & \frac{8}{b^{2}} = 1 \Rightarrow b^{2} = 8 \end{array}$

Thus, equation of required ellipse is $\frac{x^{2}}{4} + \frac{y^{2}}{8} = 1$

$∵ e = \frac{2}{b}$ Now, from the option the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{8} = 1$ passes through the point $(\sqrt{2}, 2)$ .

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अगला

Ellipse 1 Question 1

1. An ellipse, with foci at $(0, 2)$ and $(0, - 2)$ and minor axis of length 4, passes through which of the following points?

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Ellipse 1 Question 1

1. An ellipse, with foci at (0,2) and (0,−2) and minor axis of length 4, passes through which of the following points?

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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1. An ellipse, with foci at $(0, 2)$ and $(0, - 2)$ and minor axis of length 4, passes through which of the following points?