Question # 1

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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5

25

3

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Intersection of two parabolas

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parabola

Two points

Four points

Hyperobla

If t is the parameter for one end of a focal chord of the parabola y²= 4ax, then its length is

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The common point to four standard parabolas

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Focus

Centre

Vertex

P(x,y)

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

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An ellipse

A parabola

A circle

A hyperbola

The ellipse and hyperbola are called

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Concentric conics

Central conics

Both a b

None

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0

1

13

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

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The centre of the conic x2 +16x +4y2 -16y +76 =0 is

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(0,10)

(-8,4)

(-8,-2)

(1,1)

The parabola y²= x is symmetric about

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x-axis

y-axis

Both x and y-axis

The line y = x

The axis of the parabola x² = 4ay is:

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y = 0

x = 0

x = -a

y = a

Equation of parabola with focus F(-3,1) directrix x=3 is

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(y -1)2 =-12x

(y-1)2 =4x

(x+3)2 =4a(y-1)

y2 =-12(x-1)

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6

20

0

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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

For what value of k, 3x -2y+ k= 0 is tangent to the circle x2 +y2 +6x -4y =0

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k=0

k=0 or 26

k = 26

k=-13

If either A = 0 or B =0,then Ax2 +By2 +2Gx +2Fy +c =0 represents a

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Circle

Hyperbola

Ellipse

Parabola

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

The tangents drawn from the point P to a circle are real and distinct if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

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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 equation ax²+ 2hxy + by²+2gx + 2fy + c =0 represents an ellipse if

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The two different parts of the hyperbola are called its

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Vertices

Directrices

Nappes

Branches

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 line joining the center of a circle to the midpoint of the chord is

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Perpendicular to the tnagent

Perpendicular to the normal

Perpendicular to the chord

The line y = 4x + c touches the hyperbola x²- y²= 1 if

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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

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

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