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Online Tests

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

Question # 1

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Question # 2

The perpendicular bisector of any chord of a circle

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Passes through the centre of the circle

Does not pass through the centre of the circle

May or may not pass through the centre of the circle

None of these

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Question # 3

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2

4

3

16

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Question # 4

The point (x₁, y₁) lies outside the circle x²+ y²+ 2gx + 2fy + c =0 if

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Question # 5

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(-6,4)

(-3,2)

(6,-4)

(3, -2)

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Question # 6

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

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Question # 7

The equation of vertical asymptotes of y = cos ecx is

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x = 0

y = 0

x =∞

y =∞

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Question # 8

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none of these

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Question # 9

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Question # 10

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Question # 11

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Question # 12

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

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Question # 13

The conic is a parabola, when:

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ᵨ > 1

ᵨ < 1

ᵨ = 1

ᵨ = 0

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Question # 14

A square is inscribed in the circle x²+ y²- 2x + 4y + 3 =0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is

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Question # 15

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(g,f)

(-g,f)

(g,-f)

(-g,-f)

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Question # 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

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Question # 17

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

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Question # 18

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Question # 19

The constant distance of all points of the circle from its centre is called the

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Radius of the circle

Secant of the circle

Chord of the circle

Diameter of the circle

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Question # 20

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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Question # 21

The parametric equations of a circle are

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Question # 22

If (0, 0) and (-1, 0) are end points of a diameter, then the equation of the circle is

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Question # 23

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

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Question # 24

The line 3x - 4y = 0

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Is a tangent to the circle x²+ y²= 25

Is a normal to the circle x²+ y²=25

Does not meet the circle x²+ y²= 25

Does not pass thro' the origin

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Question # 25

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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Question # 26

y=-a is the equation of the directrix of

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y2 =4ax

x2=-4ay

x2=4ay

y2=-4ax

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Question # 27

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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Question # 28

If e,e′ be the eccentricities of two conics S=0 and S′ =0 and if e2 +e′2 =3 then both S and S′ can be

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Hyperbola

Parabolas

Ellipses

None of these

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Question # 29

If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve obtained is

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an ellipse

a hyperbola

a circle

a parabola

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Question # 30

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Question # 31

The eccentricity e of an ellipse is always

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Rational

Real

Irrational

Integer

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