SATHEE: Ellipse 1 Question 13

Ellipse 1 Question 13

14. If the tangents to the ellipse at $M$ and $N$ meet at $R$ and the normal to the parabola at $M$ meets the $X$ -axis at $Q$ , then the ratio of area of $△ M Q R$ to area of the quadrilateral $M F_{1} N F_{2}$ is

(a) $3 : 4$

(b) $4 : 5$

(d) $2 : 3$

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Answer:

Correct Answer: 14. (c)

Solution:

Equation of tangent at $M (3 / 2, \sqrt{6})$ to $\frac{x^{2}}{9} + \frac{y^{2}}{8} = 1$ is

$\frac{3}{2} \cdot \frac{x}{9} + \sqrt{6} \cdot \frac{y}{8} = 1$

which intersect $X$ -axis at $(6, 0)$ .

Also, equation of tangent at $N (3 / 2, - \sqrt{6})$ is

$\frac{3}{2} \cdot \frac{x}{9} - \sqrt{6} \frac{y}{8} = 1$

Eqs. (i) and (ii) intersect on $X$ -axis at $R (6, 0)$ .

Also, normal at $M (3 / 2, \sqrt{6})$ is $y - \sqrt{6} = \frac{- \sqrt{6}}{2} x - \frac{3}{2}$

On solving with $y = 0$ , we get $Q (7 / 2, 0)$

$∴$ Area of $△ M Q R = \frac{1}{2} 6 - \frac{7}{2} \sqrt{6} = \frac{5 \sqrt{6}}{4}$ sq units

and area of quadrilateral $M F_{1} N F_{2} = 2 \times \frac{1}{2} 1 - (- 1) \sqrt{6}$

$∴ \frac{Area of △ M Q R}{Area of quadrilateral M F_{1} N F_{2}} = \frac{5}{8}$ $= 2 \sqrt{6}$ sq units

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Ellipse 1 Question 13

14. If the tangents to the ellipse at $M$ and $N$ meet at $R$ and the normal to the parabola at $M$ meets the $X$ -axis at $Q$ , then the ratio of area of $△ M Q R$ to area of the quadrilateral $M F_{1} N F_{2}$ is

Answer:

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Ellipse 1 Question 13

14. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the X-axis at Q, then the ratio of area of △MQR to area of the quadrilateral MF1NF2 is

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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14. If the tangents to the ellipse at $M$ and $N$ meet at $R$ and the normal to the parabola at $M$ meets the $X$ -axis at $Q$ , then the ratio of area of $△ M Q R$ to area of the quadrilateral $M F_{1} N F_{2}$ is