SATHEE: Ellipse 1 Question 5

Ellipse 1 Question 5

6. The ellipse $E_{1} : \frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_{2}$ passing through the point $(0, 4)$ circumscribes the rectangle $R$ . The eccentricity of the ellipse $E_{2}$ is

(2012)

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

(b) $\frac{\sqrt{3}}{2}$

(d) $\frac{3}{4}$

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Answer:

Correct Answer: 6. (a)

Solution:

PLAN Equation of an ellipse is $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

Eccentricity

$e^{2} = 1 - \frac{b^{2}}{a^{2}}$

440 Ellipse

Description Situation As ellipse circumscribes the rectangle, then it must pass through all four vertices.

Let the equation of an ellipse $E_{2}$ be

$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ , where $a < b$ and $b = 4$ .

Also, it passes through $(3, 2)$ .

$\begin{array}{lll} \Rightarrow & \frac{9}{a^{2}} + \frac{4}{b^{2}} = 1 & [∵ b = 4] \\ \Rightarrow & \frac{9}{a^{2}} + \frac{1}{4} = 1 or a^{2} = 12 \end{array}$

Eccentricity of $E_{2}, e^{2} = 1 - \frac{a^{2}}{b^{2}} = 1 - \frac{12}{16} = \frac{1}{4} [∵ a < b]$

$∴ e = \frac{1}{2}$

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Ellipse 1 Question 5

6. The ellipse $E_{1} : \frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_{2}$ passing through the point $(0, 4)$ circumscribes the rectangle $R$ . The eccentricity of the ellipse $E_{2}$ is

Answer:

440 Ellipse

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एनसीईआरटी व्यायाम वीडियो समाधान

Ellipse 1 Question 5

6. The ellipse E1:x29+y24=1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point (0,4) circumscribes the rectangle R. The eccentricity of the ellipse E2 is

Answer:

440 Ellipse

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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6. The ellipse $E_{1} : \frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_{2}$ passing through the point $(0, 4)$ circumscribes the rectangle $R$ . The eccentricity of the ellipse $E_{2}$ is