Question # 1

The centre of the circle x2+y2 -2fx-2gy+x=0 is

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(-g,-f)

(g,f)

(f,g)

(-f,-g)

If (2, 3) and (2, 5) are end points of a diameter of a circle, then the centre of the circle is

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(2, 4)

(4, 8)

(0, 2)

(0, -2)

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The two different parts of the hyperbola are called its

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Vertices

Directrices

Nappes

Branches

The common point to four standard parabolas

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Focus

Centre

Vertex

P(x,y)

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

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Tangent

Vertex

Axis

None

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8

4

64

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

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Chord

Tangent

Lust rectum

directrix

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none of these

The line 2x +√6y =2 is a tangent to the curve x2 -2y2 =4 The point of contact is

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(√6,1)

(2,3)

(7,-2√6)

(4,-√6)

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

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Circle

Ellipse

Parabola

Hyoerbola

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

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The number of real tangents that can be drawn to the ellipse 3x²+ 5y²= 32 passing thro. (3, 5) is

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0

1

2

Infinite

The remove the term involving xy, from 7x2 -6√3xy+ 13y2 -16 =0 the angel of rotation is

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θ = 30°

θ = 45°

θ = 60°

θ = 75°

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

The number of standard parabolic functions are is

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4

2

3

1

An ellipse slides between two lines at right angles to one another. The locus of its centre is :

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a parabola

an ellipse

a circle

a hyperbola

A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then CP²+ CQ²+ CR²+ CS²=

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r²

2 r²

3 r²

4 r²

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5

25

3

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

The eccentricity of parabola is:

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1

0

Greater than 1

Less than 1

If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a

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parabola

circle

hyperbola

ellipse

If the circle x²+ y²+ 2gx +2fy + c = 0 passes through the origin then

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c = 0

c = -1

c = -2

c = 1

The axis of the parabola y²= 4ax is

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X = 0

Y = 0

X = y

X = -y

If a > 0 they parabola y2 =-4ax lies in

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I and iv quadrant

I quadrant

II and III quadrant

All are incorrect

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

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c =±√2

c =0

c=±√17

c=±√15

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0

1

13

The sum of the focal distance from any point on the ellipse 9x2 +16y2 =144 is

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32

16

18

8

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The constant distance of all points of the circle from its centre is called the

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Radius of the circle

Secant of the circle

Chord of the circle

Diameter of the circle

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

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