Question # 1

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

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2

4

6

8

What is the axis of the parabola y²= 4ax?

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x = 0

y = 0

x = a

y = 0

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

If a > 0 they parabola y2 =-4ax lies in

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I and iv quadrant

I quadrant

II and III quadrant

All are incorrect

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none of these

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none of these

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)

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The slope of the normal at the point (at², 2at) of the parabola y²= 4ax is

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1/t

t

-t

-1/t

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 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 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

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

ᵨ is a

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variable

Positive constant

Positive variable

Directrix

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

Equation of normal to the circle x2 + y2 =25 at (5cosθ,5sinθ)

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xcosθ+ysinθ =5

xcosθ -ysinθ =0

xsinθ -ycosθ =0

None of these

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c = 0

c = -1

c = -2

c = 1

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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0

1

13

Two circles are said to be concentric if they have

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same radius

same chord

same centre

same diameter

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11

61

1

A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then CP²+ CQ²+ CR²+ CS²=

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r²

2 r²

3 r²

4 r²

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

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Chord

Tangent

Lust rectum

directrix

A line segment whose end points lie on a circle is called

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the secant of the circle

the arc of the circle

the chord of the circle

the circumference of the circle

The number of standard parabolic functions are is

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4

2

3

1

The eccentricity of parabola is:

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1

0

Greater than 1

Less than 1

The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is

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A parabola

A circle

An ellipse

A st. line

If the focus lies on the y-axis with coordinates f(0,a) and directrix of the parabola is y = -a, the equation of parabola is:

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y² = -4 ax

x² = 4ay

x² = -4ay

y² = 4ax

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

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