Question # 1

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

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

The length of the tangent from (2, 1) to the circle x²+ y²+ 4y + 3 = 0 is

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If the distance of any point on the curve from any of the two lines approaches zero then it is called

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Axis

Directrices

Asymptotes

None

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

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

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

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)

The parabola y2 + 2y + x = 0 lie in _____ quadrant.

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First

Second

Third

Fourth

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A parabola

An ellipse

A hyperbola

A circle

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

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-a

a

a/2

0

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An ellipse

A parabola

A circle

A hyperbola

If the focus lies on the y-axis with coordinates f(0,a) and directrix of the parabola is y = -a, the equation of parabola is:

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y² = -4 ax

x² = 4ay

x² = -4ay

y² = 4ax

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

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2

4

3

16

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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Two circles x2 +y2 +8x -9= 0 and x2+y2+6y +k =0 touchinternallyif the value of k is

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k = 9

k = ±9

k=-9

k=11

The axis of the parabola x² = 4ay is:

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y = 0

x = 0

x = -a

y = a

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none of these

The common point to four standard parabolas

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Focus

Centre

Vertex

P(x,y)

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Latus rectum = 4 x ______________

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focal distance of the vertex

Chord

Focus

1/2

The eccentricity of the parabola y²= -8x is

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-2

2

-1

1

The lotus of intersection of perpendicular tangents to the parabola y² = 4ax is:

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Axis of the parabola

Focal chord of the parabos

The tangent at vertex of the parabola

a directrix of the parabola

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

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Circle

Ellipse

Parabola

Hyoerbola

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

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m=1

m=2

m=3

m=4

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1

5

7

9

The parabola y²= x is symmetric about

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x-axis

y-axis

Both x and y-axis

The line y = x

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11

61

1

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