Question # 1

A circle is a limiting case of an ellipse whose eccentricity

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Tends to a

Tends to b

Tends to 0

Tends to a + b

The eccentricity of the conic 9x²- 16y²= 144 is

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4/5

5/4

4/3

3/4

Ifᵨ> 1 , then the conic, is:

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Ellipse

Parabola

Hyperbola

None of these

The eccentricity of ellipse becomes zero, then it takes the form of:

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a parabols

a straight line

a circle

None of these

The line y = 4x + c touches the hyperbola x²- y²= 1 if

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1

5

7

9

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2 b

2 a

2 ab

a + b

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none of these

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The number of standard parabolic functions are is

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4

2

3

1

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0

1

13

x =r cosθ,y= sinθ are the parametric equations of

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Circle

Ellipse

Parabola

Hyoerbola

The equation of the tangent at vertex to the parabola is y2 = -8(x -3)

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y=0

x=3

x=1

x=5

The span of a standard parabola depends upon

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x

a

y

y2

The perpendicular bisector of any chord of a circle

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Passes through the centre of the circle

Does not pass through the centre of the circle

May or may not pass through the centre of the circle

None of these

The end points of the major axis of the ellipse are called its

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Foci

Vertices

Co - vertices

None of these

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If the line 2x -y +k =0 is a diameter of the circle x2 +y2 +6x -6y +5 =0 then k is equal to

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12

9

6

3

What is the axis of the parabola y²= 4ax?

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x = 0

y = 0

x = a

y = 0

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The line Ax + By + C = 0 will touch the circle x²+ y²=λ when

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C²=λ(A²+ B²)

A²=λ(A²+ C²)

B²=λ(A²+ C²)

None of these

Two circles x2 +y2 +8x -9= 0 and x2+y2+6y +k =0 touchinternallyif the value of k is

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k = 9

k = ±9

k=-9

k=11

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none of these

ax2 +2hxy +by2 +2gx +2fy +c =0 may represent an ellipse if

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h2 -ab <0

h2 -ab≠ 0

h2 -ab =0

h2 -ab >0

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none of these

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11

61

1

The equation of the circle with centre (-h, -k) and radius r is

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(x +h)²+ (y+k)²= r²

(x +h)²+ (y-k)²= r²

(x -h)²+ (y+k)²= r²

(x -h)²+ (y-k)²= r²

A line joining two distinct points on a parabola is called a ______ of the parabola.

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Chord

Tangent

Lust rectum

directrix

The equation of the parabola with directirx x = 2 and the axis y = 0 is

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y²= 8x

y²= -8x

y²= 4x

y²= -4x

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