Question # 1

If the equation of the parabola x² = 4ay, then opening of the parabola is upward of the:

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x-axis

y-axis

Major axis

Minor axis

The graph of the the parabola x² = 4ay lies in quadrant:

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I and II

III and IV

II and III

I and III

The focus of the parabola x² = 4ay:

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(0, a)

(-a , 0)

(0, -a)

(a, 0)

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 chord containing the center of the circle is called ______ of the circle:

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Diameter

Chord

Radius

None of these

The equation x² + y² + 2x + 3y = 10 represents a:

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A pair of lines

Circle

Ellipse

Hyperbola

If r is the radius of any circle and C its center, then any point P(x₁, y₁) lies on the circle only if:

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|CP| < r

|CP| > r

|CP| = r

None of these

If the equation of the parabola is y2 = 4ax, then opening of the parabola is to the right of the:

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x-axis

y = x

y-axis

x + y =0

The condition for the line y = mx + c to be a tangent to the circle x² + y² = a² is c = _____________:

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The directrix of the parabola y² = 4ax is:

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x = a

x = -a

y = a

y = - a

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

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x = a

x = -a

y = a

y = -a

Point p (-5, 6) lies ............ the circle x² + y² + 4x - 6y - 12 = 0

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Outside

Inside

On

None of these

If the radius of a circle is zero, then the circle is called a / an:

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Circle

Circular cone

Ellipse

Point circle

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0

4

7

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

A line through a point say P perpendicular to the tangent to the curve at P is called:

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Straight line

Tangent line

Normal line

None of these

The fixed point of the conic is called:

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Directrix

Vertex

Focus

None of these

The axis of the parabola y² = 4ax is:

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x = 0

x = a

y = 0

y = a

The focus of the parabola y²=4ax is:

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(-a , 0)

(0, a)

(0, -a)

(a, 0)

The opening of the parabola y² = -4ax is to the left of the:

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x-axis

x = 1

y-axis

x = 0

In equation of circle, coefficient of each of x² and y² are:

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Not equal

Opposite in signs

Equal

None of these

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