Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-2>Q 1

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A line segment of fixed length $a + b$ moves so that its ends are always on two fixed perpendicular straight lines, then the locus of a point, which divides this line into portions of length $a$ and $b$ , is

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Important Questions on Ellipse

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-2>Q 2

The locus of the point of intersection of tangents to an ellipse

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

at two points, sum of whose eccentric angles is constant, is a/an

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-2>Q 3

An ellipse with major axis

4

and minor axis

2

touches both the coordinate axis, then locus of its centre is

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-2>Q 4

An ellipse with major axis

4

and minor axis

2

touches both the coordinate axes, then locus of its focus is

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-2>Q 7

If

(0,3 + \sqrt{5})

is a point on the ellipse whose foci are

(2,3)

and

(- 2,3)

, then the length of the semi-major axis is

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-2>Q 8

A circle has the same centre as an ellipse & passes through the focii

F_{1} & F_{2}

of the ellipse, such that the two curves intersect at

4

points. Let

' P'

be any one of their points of intersection. If the major axis of the ellipse is

17

& the area of the triangle

P F_{1} F_{2}

is

30

, then the distance between the focii is

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-2>Q 9

Point

' O'

is the centre of the ellipse with major axis

A B

& minor axis

C D

. Point

F

is one focus of the ellipse. If

O F = 6

& the diameter of the inscribed circle of triangle

O C F

is

2

, then the product

(A B) (C D)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-2>Q 10

If '

r

' be the radius of largest circle with centre

(3, 0)

that can be inscribed in the ellipse

9 x^{2} + 25 y^{2} = 225

, then

4 \sqrt{7} r

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-2>Q 11

Minimum length of the intercept made by the axes on the tangent to the ellipse

\frac{x^{2}}{81} + \frac{y^{2}}{36} = 1

is equal to