Question # 1

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The equation of the normal to the circle x²+ y²= 25 at (4, 3) is

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3x - 4y =0

3x - 4y =5

4x + 3y = 5

4x + 3y = 25

The two different parts of the hyperbola are called its

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Vertices

Directrices

Nappes

Branches

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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 general equation of a circle is

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the curve of the parabola y² = -4ax is symmetric with respect to

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x -axis

y - axis

Botha x and y- axis

None of thes

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)

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

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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1

5

7

9

If eccentricity of ellipse becomes zero then it takes the form of

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A parabola

A circle

A straight line

None of these

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The tangent to the parabola y2 =4ax and perpendicular line from the focus on it meet

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x =0

y =0

x =-9

y = -a

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

The eccentricity of the parabola y²= -8x is

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-2

2

-1

1

y=-a is the equation of the directrix of

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y2 =4ax

x2=-4ay

x2=4ay

y2=-4ax

The vertex of the equation y² = 4ax is:

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(2, -2)

(1,1)

(0 , 0)

(2 , 2)

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A square is inscribed in the circle x²+ y²- 2x + 4y + 3 =0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is

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8

4

64

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

Two circles are said to be concentric if they have

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same radius

same chord

same centre

same diameter

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

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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

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(g,f)

(-g,f)

(g,-f)

(-g,-f)

The axis of the parabola x² = 4ay is:

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y = 0

x = 0

x = -a

y = a

The tangents drawn from the point P to a circle are imaginary if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

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

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

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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