Question # 1

A line joining two distinct points on a parabola is called

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Axis

Directrix

Chord

Tangent

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

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 equation of vertical asymptotes of y = cos ecx is

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x = 0

y = 0

x =∞

y =∞

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

The eccentricity e of an ellipse is always

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Rational

Real

Irrational

Integer

a chord passing through the focus of a parabola is called a:

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Focal chord

Latus rectum

Tangent

Directrix

ᵨ is a

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variable

Positive constant

Positive variable

Directrix

The parabola y2 + 2y + x = 0 lie in _____ quadrant.

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First

Second

Third

Fourth

The end points of the major axis of the ellipse are called its

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Foci

Vertices

Co - vertices

None of these

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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The slope of the tangent at the point (h,h) of the circle x2 +y2 =a2 is

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0

1

-1

h

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

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

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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

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

The distance of point P(x,y) from focus in a parabola

y² =4ax, is:

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2a

a

x + a

x-a

The conic is a parabola if

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e < 1

e > 1

e = 1

None of these

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2 b

2 a

2 ab

a + b

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

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The parabola y²= x is symmetric about

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x-axis

y-axis

Both x and y-axis

The line y = x

The locus of the centre of a circle which touches two given circles externally is:

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a hyperbola

an ellipse

a circle

a parabola

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

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8

4

64

None of these

The line through the centre and perpendicular to the transverse axis is called the

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Major axis

Minor axis

Focal axis

Conjugate axis

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(-6,4)

(-3,2)

(6,-4)

(3, -2)

The point which is closet to the focus of a parabola is:

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vertex

Chord

Focus

Directix

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

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

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