Question # 1

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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

The number of tangents to the circle x2+ y2 -8x -6y +9 =0 which pass through the point (3,-2) is

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2

1

0

None of these

Number of conics is

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1

3

2

4

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

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vertex

Chord

Focus

Directix

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 vertex of the equation y² = 4ax is:

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(2, -2)

(1,1)

(0 , 0)

(2 , 2)

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)

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

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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

The locus of the centre of a circle which touches two given circles externally is:

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a hyperbola

an ellipse

a circle

a parabola

The circle (x - 2)²+ (y + 3)²= 4 is not concentric with the circle

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(x - 2)²+ (y + 3)²= 9

(x + 2)²+ (y - 3)²= 4

(x + 2)²+ (y - 3)²= 8

(x - 2)²+ (y + 3)²= 5

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

The eccentricity e of an ellipse is always

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Rational

Real

Irrational

Integer

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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)

An ellipse slides between two lines at right angles to one another. The locus of its centre is :

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a parabola

an ellipse

a circle

a hyperbola

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8

4

64

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c = 0

c = -1

c = -2

c = 1

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

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none of these

The conic ax2+2hxy+by2+2gx+2fy+c= 0 never represent a circle if

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a≠ b,h≠0

a=b

h≠0

h=0

The ellipse and hyperbola are called

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Concentric conics

Central conics

Both a b

None

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

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(1, 3)

(-1, -3)

(1, -3)

(-1, 3)

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

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 vertices of the ellipse x²+ 4y²= 16 are

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If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

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an ellipse

a hyperbola

a 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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