Question # 1

If x + y + 1 = 0 touches the parabola y²=λx, thenλis equal to

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2

4

6

8

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none of these

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 locus of the centre of a circle which touches two given circles externally is:

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a hyperbola

an ellipse

a circle

a parabola

The span of a standard parabola depends upon

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x

a

y

y2

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184

none of these

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

The vertices of the ellipse x²+ 4y²= 16 are

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The straight line passing through the focus and perpendicular to the directrix of the conic is known as its

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Tangent

axis

Focal chord

major or manor axis

If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve obtained is

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an ellipse

a hyperbola

a circle

a parabola

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An ellipse

A parabola

A circle

A hyperbola

Coordinates of the focus of the parabola x² - 4x -8y-4=0 are:

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(0,2)

(,0,1)

(2,0)

(1,2)

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

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 slope of the normal at the point (at², 2at) of the parabola y²= 4ax is

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1/t

t

-t

-1/t

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

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none of these

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

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°

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If (0, 0) and (1, 0) are the end points of a diameter, then the equation of the circle is

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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

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(1, 3)

(-1, -3)

(1, -3)

(-1, 3)

The point on y²= 4ax nearest to the focus has its abciassae equal to

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-a

a

a/2

0

The number of standard parabolic functions are is

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4

2

3

1

Ifᵨ> 1 , then the conic, is:

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Ellipse

Parabola

Hyperbola

None of these

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

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Circle

Hyperbola

Ellipse

Pair of straight lines

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

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