Question # 1

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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

If (a, b) is the mid-point of a chord passing thro' the vertex of the parabola y²= 4x, then

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a = 2b

2a = b

a²= 2b

2a = b²

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

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Foci

Vertices

Co - vertices

None of these

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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c = 0

c = -1

c = -2

c = 1

If (2,0) is the vertex and y-axis is directrix of parabola then focus is

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(2,0)

(-2,0)

(4,0)

(-4,0)

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°

Area of the circle with ends of a diameter at (-3,2) and (5,-6)

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128π sq. units

64π sq. units

32π sq.units

None of these

The point (x₁, y₁) lies outside the circle x²+ y²+ 2gx + 2fy + c =0 if

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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 parabola is:

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1

0

Greater than 1

Less than 1

The line y =mx +1 is tangent to the parabola y2 =4x if

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m=1

m=2

m=3

m=4

If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____

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12

8

24

-24

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

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The equation of a line parallel to the tangent to the circle x²+ y²= 16 at the point (2, 3) and passing thro' the origin is

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2x + 3y = 0

2x - 3y = 0

3x + 2y = 0

3x - 2y = 0

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 number of standard parabolic functions are is

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4

2

3

1

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none of these

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none of these

A line joining two distinct points on a parabola is called

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Axis

Directrix

Chord

Tangent

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

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 common point to four standard parabolas

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Focus

Centre

Vertex

P(x,y)

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c = 0

c = -1

c = -2

c = 1

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A chord passing through the centre of the circle is called

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the secant of the circle

the tangent of the circle

the arc of the circle

the diameter of the circle

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)

If the st. line 3x + 4y = K touches the circle x²+ y²- 10x = 0 then the value of K is

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-1 or 20

-10 or 40

-2 or 20

2 or 20

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