Question # 1

The axis of the parabola y²= 4ax is

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X = 0

Y = 0

X = y

X = -y

The equation of a line parallel to the tangent to the circle x²+ y²= 16 at the point (2, 3) and passing thro' the origin is

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2x + 3y = 0

2x - 3y = 0

3x + 2y = 0

3x - 2y = 0

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none of these

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(1, 3)

(-1, -3)

(1, -3)

(-1, 3)

The line y =mx +1 is tangent to the parabola y2 =4x if

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m=1

m=2

m=3

m=4

The general equation of a circle is

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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°

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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

A line joining two distinct points on a parabola is called a ______ of the parabola.

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Chord

Tangent

Lust rectum

directrix

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 conic is a parabola if

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e < 1

e > 1

e = 1

None of these

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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none of these

y=-a is the equation of the directrix of

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y2 =4ax

x2=-4ay

x2=4ay

y2=-4ax

The directrix of y2 =-4ax is

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y =-a

y = a

x = a

x = -a

The eccentricity e of an ellipse is always

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Rational

Real

Irrational

Integer

Intersection of two parabolas

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parabola

Two points

Four points

Hyperobla

Ifᵨ> 1 , then the conic, is:

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Ellipse

Parabola

Hyperbola

None of these

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

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Circle

Ellipse

Parabola

Hyoerbola

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An ellipse

A parabola

A circle

A hyperbola

The vertex of the parabola (xsin a -ycos a)2 =4a(xcos a +ysin a) lies at

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(acos a,asin a)

(a,0)

(cos a,sin a)

(0,0)

The eccentricity of parabola is:

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1

0

Greater than 1

Less than 1

The parametric equations of a circle are

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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 radius of the circle (x - 1)²+ (y + 3)²= 61 is

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8

4

64

None of these

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2

4

3

16

The area of the circle centred at (1,2) and passing through (4,6) is

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30 πsq.units

5π sq.units

15π sq.units

25π sq.units

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

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

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