Question # 1

The curves obtained by cutting a __________ double right circular cone by a _______ are called conics:

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Straight line

Plane

Curve

None of these

In the case of rotation of axes which formula is true:

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y² = 4ax, is the standard equation of the:

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Ellipse

Parabola

Hyperbola

None of these

Length of tangent from (a, 0) to the circle x² + y² + 2gx + 2fy + c = 0 is:

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c

2g + 2f -c

None

The axis of the parabola x² = 4ay is:

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x = 0

x = -a

y = 0

y = -a

The equi. of latus-rectum of the parabola y² = -4ax is:

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x = a

x = -a

y = a

y = -a

If the equation of the parabola is y² = - 4ax, then opening of the parabola is to the ______ of the y-axis:

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Left

Upward

Right

Downward

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a

2b

b

2a

Two imaginary tangents can be drawn to a circle from any point P(x₁, y₁) _______ the circle:

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Inside

On

Outside

None of these

A line segment whose end points lie on the circle is called a __________ of the circle.

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Radius

Chord

Diameter

None of these

The fixed point of the conic is called:

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Directrix

Vertex

Focus

None of these

The opening of the parabola x² = 4ay is upward of the:

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x -axis

y = c

y - axis

x = y

Perpendicular dropped from the center of a circle on a chord _______ the chord:

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Normal

Bisects

Equal to

None of these

The vertex of parabola (x - 1)² = 8 (y + 2) is:

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(1, -2)

(0, 1)

(-1, -2)

(1, 2)

The axis of the parabola y² = 4ax is:

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x = 0

x = a

y = 0

y = a

Two arcs of two different circles are congruent if:

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The circles are congruent

The corresponding central angles are congruent

Both a and b

None of the above

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

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Directrix

Latus rectum

Focus

Focal chord

The directrix of the parabola y² = 4ax is:

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x = a

x = -a

y = a

y = - a

The number e denotes the _______ of the conic:

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Directrix

Vertex

Focus

Eccentricity

The radius of circle x² + y² + ax + by + c = 0 is:

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None

Equation of axis of the parabola x² = 4ay is:

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x = 0

x = a

y = 0

y = a

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