Question # 1

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

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Circle

Ellipse

Parabola

Hyoerbola

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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 number of standard parabolic functions are is

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4

2

3

1

The line through the focus and perpendicular to the directrix is called ______ of the parabola

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axis

focal chord

tangent

latus rectum

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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

The equation of the circle wit (-1, 1) and radius 2 is

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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 equation of vertical asymptotes of y = cos ecx is

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x = 0

y = 0

x =∞

y =∞

The equation x²+ y²= 0 represents

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A circle

A degenerate circle

An empty set

A st. line

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none of these

The span of a standard parabola depends upon

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x

a

y

y2

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The number of tangents to the circle x2+ y2 -8x -6y +9 =0 which pass through the point (3,-2) is

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2

1

0

None of these

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

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an ellipse

a hyperbola

a circle

a parabola

If the vertex of the parabola is the origin and directrix is x+5 = 0 . then its latus rectum is:

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10

5

0

20

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

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x = 0

y = 0

x = a

y = 0

The fixed point from which all the points of a circle are equidistant is called the

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chord of the circle

centre of the circle

diameter of the circle

radius of the circle

If (x₁, y₁) and (x₂,y₂) are the end points of a diameter then the centre of the circle is

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The common point to four standard parabolas

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Focus

Centre

Vertex

P(x,y)

If a plane passes through the vertex of a cone then the intersection is

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an ellipse

a hyperbola

a point circle

a parabola

the latus rectum of the parabola x³= -4ay is:

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x = a

y = -a

x = -a

y = 0

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c = 0

c = -1

c = -2

c = 1

The equation x2+ y2- 8x+ 6y+ 25= 0 represents

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A circle

A pair of straight lines

A point

None of these

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Ifᵨ> 1 , then the conic, is:

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Ellipse

Parabola

Hyperbola

None of these

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

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The equation ax²+ 2hxy + by²+2gx + 2fy + c =0 represents an ellipse if

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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

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184

none of these

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

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