Question # 1

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If the cutting plane is slightly tilted and cuts only one nappe of the cone, the intersection is

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an ellipse

a hyperbola

a circle

a parabola

The line Ax + By + C = 0 will touch the circle x²+ y²=λ when

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C²=λ(A²+ B²)

A²=λ(A²+ C²)

B²=λ(A²+ C²)

None of these

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)

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

The eccentricity of the conic 9x²- 16y²= 144 is

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4/5

5/4

4/3

3/4

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0

1

13

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

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The parabolay2=4ax open up if

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a<0

a≠0

a>0

All are incorrect

The straight line passing through the focus and perpendicular to the directrix of the conic is known as its

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Tangent

axis

Focal chord

major or manor axis

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6

20

0

If (a, b) is the mid-point of a chord passing thro' the vertex of the parabola y²= 4x, then

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a = 2b

2a = b

a²= 2b

2a = b²

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

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 (x₁, y₁) and (x₂,y₂) are the end points of a diameter then the centre of the circle is

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none of these

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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y=0 of the parabola y² = 4ax is the

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equation of directirx

Equatio of the tangent

Equation of axis

equation of latus rectum

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

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The remove the term involving xy, from 7x2 -6√3xy+ 13y2 -16 =0 the angel of rotation is

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θ = 30°

θ = 45°

θ = 60°

θ = 75°

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 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

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 axis of the parabola y²= 4ax is

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X = 0

Y = 0

X = y

X = -y

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 equation of vertical asymptotes of y = cos ecx is

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x = 0

y = 0

x =∞

y =∞

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

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