Question # 1

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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The point on y²= 4ax nearest to the focus has its abciassae equal to

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-a

a

a/2

0

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

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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

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(g,f)

(-g,f)

(g,-f)

(-g,-f)

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

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c = 0

c = -1

c = -2

c = 1

The vertices of the ellipse x²+ 4y²= 16 are

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Co-ordinate of a point on the parabola y² = 8x whose focal distance is 4 are:

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(2 , 4)

(-2 ,-4)

(-2, 4)

(2,-4)

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An ellipse

A parabola

A circle

A hyperbola

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)

ax2 +2hxy +by2 +2gx +2fy +c =0 may represent an ellipse if

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h2 -ab <0

h2 -ab≠ 0

h2 -ab =0

h2 -ab >0

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the latus rectum of the parabola x³= -4ay is:

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x = a

y = -a

x = -a

y = 0

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8

4

64

Area of the circle with ends of a diameter at (-3,2) and (5,-6)

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128π sq. units

64π sq. units

32π sq.units

None of these

If x + y + 1 = 0 touches the parabola y²=λx, thenλis equal to

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2

4

6

8

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6

20

0

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none of these

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The equation of the circle with centre (h, k) and radius r is

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(x+ h)²+ (y+ k)²= r²

(x+ h)²+ (y - k)²= r²

(x - h)²+ (y+ k)²= r²

(x - h)²+ (y - k)²= r²

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

The parabolay2=4ax open up if

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a<0

a≠0

a>0

All are incorrect

The equation of the tangent at vertex to the parabola is y2 = -8(x -3)

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y=0

x=3

x=1

x=5

If the st. line 3x + 4y = K touches the circle x²+ y²- 10x = 0 then the value of K is

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-1 or 20

-10 or 40

-2 or 20

2 or 20

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(1, 3)

(-1, -3)

(1, -3)

(-1, 3)

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

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Chord

Tangent

Lust rectum

directrix

Intersection of two parabolas

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parabola

Two points

Four points

Hyperobla

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

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A line joining two distinct points on a parabola is called

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Axis

Directrix

Chord

Tangent

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

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