Question # 1

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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(-6,4)

(-3,2)

(6,-4)

(3, -2)

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none of these

If t is the parameter for one end of a focal chord of the parabola y²= 4ax, then its length is

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A parabola

An ellipse

A hyperbola

A circle

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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)

If the vertex of the parabola is the origin and directrix is x+5 = 0 . then its latus rectum is:

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10

5

0

20

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

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(g,f)

(-g,f)

(g,-f)

(-g,-f)

The eccentricity of ellipse becomes zero, then it takes the form of:

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a parabols

a straight line

a circle

None of these

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none of these

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none of these

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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 tangents drawn from the point P to a circle are imaginary if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

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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 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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none of these

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 eccentricity of ellipse becomes zero then it takes the form of

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A parabola

A circle

A straight line

None of these

The tangents drawn from the point P to a circle are real and coincident if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

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

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x = a

y = -a

x = -a

y = 0

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 line 2x +√6y =2 is a tangent to the curve x2 -2y2 =4 The point of contact is

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(√6,1)

(2,3)

(7,-2√6)

(4,-√6)

The parabolay2=4ax open up if

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a<0

a≠0

a>0

All are incorrect

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

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

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

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