Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 32

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The position of the point $(1, 3)$ with respect to the ellipse $4 x^{2} + 9 y^{2} - 16 x - 54 y + 61 = 0$

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Important Questions on Ellipse

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 33

Equation of auxilliary circle of the ellipse

2 x^{2} + 6 x y + 5 y^{2} = 1

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 34

Statement-1 : Eccentricity of ellipse whose length of latus rectum is same as distance between foci is $2 \sin 18 °$ .

Statement-2 : For $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,$ eccentricity $e = \sqrt{1 - \frac{b^{2}}{a^{2}}}$ .

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 35

The curve represented by

x = 3 (\cos t + \sin t)

,

y = 4 (\cos t - \sin t)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 36

Identify the following statements for true/false (T/F) in order

S 1 :

A latus rectum of an ellipse is a line passing through a focus

S 2 :

A latus rectum of an ellipse is a line through the centre

S 3 :

A latus rectum of an ellipse is a line perpendicular to the major axis

S 4 :

A latus rectum of an ellipse is a line parallel to the minor axis

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 37

The set of values of

a

' for which

(13 x - 1)^{2} + (13 y - 2)^{2} = a (5 x + 12 y - 1)^{2}

represents an ellipse is

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 39

The distance of the point of contact from the origin of the line

y = x - \sqrt{7}

with the ellipse

3 x^{2} + 4 y^{2} = 12

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 40

If

\frac{x}{a} + \frac{y}{b} = \sqrt{2}

touches the ellipse

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

at a point

P,

then eccentric angle of

P

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 43

The equation of the chord of the ellipse

2 x^{2} + 5 y^{2} = 20

which is bisected at the point

(2, 1)

is