Question # 1

The span of a standard parabola depends upon

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x

a

y

y2

Two circles are said to be concentric if they have

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same radius

same chord

same centre

same diameter

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

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

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A parabola

An ellipse

A hyperbola

A circle

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

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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

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 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 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 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 equation of the circle witch centre (-3, 5) and radius 7 is

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(x-3)²+ (y+5)²= 7²

(x-3)²+ (y-5)²= 7²

(x+3)²+ (y+5)²= 7²

(x+3)²+ (y-5)²= 7²

Ifᵨ> 1 , then the conic, is:

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Ellipse

Parabola

Hyperbola

None of these

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

Which shape of the following objects are approximately parabolic ares?

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Light reflectors

Force

Weight of the pendul

None of these

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An ellipse

A parabola

A circle

A hyperbola

The eccentricity of the conic 9x²- 16y²= 144 is

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4/5

5/4

4/3

3/4

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

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 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

If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve obtained is

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an ellipse

a hyperbola

a circle

a parabola

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 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

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

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

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10 / 3

5 / 3

3 / 5

3 / 10

If (2, 3) and (2, 5) are end points of a diameter of a circle, then the centre of the circle is

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(2, 4)

(4, 8)

(0, 2)

(0, -2)

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0

1

13

For what value of k, 3x -2y+ k= 0 is tangent to the circle x2 +y2 +6x -4y =0

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k=0

k=0 or 26

k = 26

k=-13

The eccentricity of parabola is:

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1

0

Greater than 1

Less than 1

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2 b

2 a

2 ab

a + b

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