Question # 1

The equation of the circle wit (-1, 1) and radius 2 is

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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 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 latus rectum of the ellipse 5x²+ 9y²= 45 is

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10 / 3

5 / 3

3 / 5

3 / 10

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

The two different parts of the hyperbola are called its

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Vertices

Directrices

Nappes

Branches

Equation of the chord of contact to the tangents drawn from (-3,4) to the circle x2 + y2 = 21

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-3x + 4y =21

4x - 3x = 0

-3x + 4y = 25

None of these

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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

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c = 0

c = -1

c = -2

c = 1

The eccentricity e of an ellipse is always

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Rational

Real

Irrational

Integer

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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The number of tangents to the circle x2+ y2 -8x -6y +9 =0 which pass through the point (3,-2) is

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2

1

0

None of these

Latus rectum = 4 x ______________

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focal distance of the vertex

Chord

Focus

1/2

x =r cosθ,y= sinθ are the parametric equations of

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Circle

Ellipse

Parabola

Hyoerbola

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

The directrix of y2 =-4ax is

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y =-a

y = a

x = a

x = -a

The equation of the directrix of the parabola x²= 4ay is

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x + a = 0

x - a = 0

y + a = 0

y - a = 0

The equation x2+ y2- 8x+ 6y+ 25= 0 represents

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A circle

A pair of straight lines

A point

None of these

The equation of the chord of the circle x²+ y²- 4x = 0 whose mid-point is (1, 0) is

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y = 2

y = 1

x = 2

x = 1

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

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none of these

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

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Foci

Vertices

Co - vertices

None of these

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(1, 3)

(-1, -3)

(1, -3)

(-1, 3)

The circle (x - 2)²+ (y + 3)²= 4 is not concentric with the circle

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(x - 2)²+ (y + 3)²= 9

(x + 2)²+ (y - 3)²= 4

(x + 2)²+ (y - 3)²= 8

(x - 2)²+ (y + 3)²= 5

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

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-a

a

a/2

0

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

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The tangents drawn from the point P to a circle are real and distinct 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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ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test MCQs With Answers

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