Question # 1

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8

4

64

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Co-ordinate of a point on the parabola y² = 8x whose focal distance is 4 are:

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(2 , 4)

(-2 ,-4)

(-2, 4)

(2,-4)

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

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

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

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Circle

Ellipse

Parabola

Hyoerbola

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 line 2x -y +k =0 is a diameter of the circle x2 +y2 +6x -6y +5 =0 then k is equal to

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12

9

6

3

The second degree equation of the form Ax2 +By2 +Gx +Fy +C =0 represent hyperbola if

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A = B≠ 0

A≠ B and both are of same sign

A≠ B both are of opposite sign

Either A = 0 or B =0

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none of these

The parametric equations of a circle are

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y=-a is the equation of the directrix of

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y2 =4ax

x2=-4ay

x2=4ay

y2=-4ax

The eccentricity of ellipse becomes zero, then it takes the form of:

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a parabols

a straight line

a circle

None of these

Two tangents drawn from (2,3) to the circle x2+y2 =9 are

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Real and distinct

Imaginary

Real and coincident

None of these

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

Ifᵨ> 1 , then the conic, is:

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Ellipse

Parabola

Hyperbola

None of these

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

The parabolay2=4ax open up if

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a<0

a≠0

a>0

All are incorrect

Equation of the chord of contact to the tangents drawn from (-3,4) to the circle x2 + y2 = 21

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-3x + 4y =21

4x - 3x = 0

-3x + 4y = 25

None of these

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

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Number of conics is

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1

3

2

4

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

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)

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none of these

The point which is closet to the focus of a parabola is:

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vertex

Chord

Focus

Directix

I f the focus is F ( 0,-a) and directrix is the line v=a, then equation of the parabola is:

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x² = 4ay

y² = 4ax

y² = -4ax

x² = 4ax

The axis of the parabola x² = 4ay is:

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y = 0

x = 0

x = -a

y = a

Which shape of the following objects are approximately parabolic ares?

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Light reflectors

Force

Weight of the pendul

None of these

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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

The directrix of y2 =-4ax is

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y =-a

y = a

x = a

x = -a

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

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