Question # 1

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6

20

0

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184

none of these

ᵨ is a

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variable

Positive constant

Positive variable

Directrix

The equation of the circle with centre (5, -2) and radius 4 is

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(x-5)²+ (y+2)²= 16

(x-5)²+ (y+2)²= 4

(x-5)²+ (y-2)²= 16

(x-5)²+ (y-2)²= 4

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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 second degree equation 2x2 -xy+ 5x -2y +2 =0 represents

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Circle

Hyperbola

Ellipse

Pair of straight lines

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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

A line segment whose end points lie on a circle is called

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The secant of the circle

The arc of the circle

The chord of the circle

The circumference of the circle

For the parabola the line through focus and perpendicular to the directrix is called

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Tangent

Vertex

Axis

None

The ellipse and hyperbola are called

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Concentric conics

Central conics

Both a b

None

Two circle s1: x2+ y2 +2x- 2y- 7= 0: s2: x2+ y2- 6x+ 4y+ 9= 0

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Touch externally

Touch internally

Intersects each other

Do not intersects

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

Which shape of the following objects are approximately parabolic ares?

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Light reflectors

Force

Weight of the pendul

None of these

The parametric equations of a circle are

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8

4

64

The area of the circle centred at (1,2) and passing through (4,6) is

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30 πsq.units

5π sq.units

15π sq.units

25π sq.units

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none of these

If the cutting plane is slightly tilted and cuts only one nappe of the cone, the intersection is

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an ellipse

a hyperbola

a circle

a parabola

The conic is a parabola if

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e < 1

e > 1

e = 1

None of these

If t is the parameter for one end of a focal chord of the parabola y²= 4ax, then its length is

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The equation of vertical asymptotes of y = cos ecx is

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x = 0

y = 0

x =∞

y =∞

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

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2

4

3

16

The eccentricity of parabola is:

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1

0

Greater than 1

Less than 1

Latus rectum = 4 x ______________

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focal distance of the vertex

Chord

Focus

1/2

If (0,4) and (0,2) are vertex and focus of the parabola respectively, the the equation of the parabola is:

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x² = 4y -32

x² =8y -32

y³ = 16 x

x2 + 8y =32

The directrix of y2 =-4ax is

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y =-a

y = a

x = a

x = -a

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

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ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test MCQs With Answers

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