Question # 1

The directrix of the parabola y² = 4ax is:

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x = a

x = -a

y = a

y = - a

The graph of the parabola y² = -4ax lies in quadrants:

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I and II

III and IV

II and III

I and III

A line that touches the curve without cutting through it is called:

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Straight line

Tangent line

Normal line

Vertical line

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

The ratio between the measure of the radial segment and the diameter of a circle is:

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2 : 1

4 : 3

1 : 2

The focus of the parabola y²=4ax is:

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(-a , 0)

(0, a)

(0, -a)

(a, 0)

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0

4

7

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

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a

4a

2a

None of these

Point (5, 6) lies ..... the circle x² + y² = 81:

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Outside

Inside

On

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

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 focus lies on the x-axis with coordinates F(a, 0) and directrix of the parabola is = - a then the equation of parabola is:

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x² = 4ay

y²= 4ax

-x²= 4ay

-y²= 4ax

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

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Length of tangent from (0,1) to x² + y² + 6x - 3y + 3 = 0

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2

1

4

3

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the section a / an:

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Parabola

Hyperbola

Ellipse

None of these

The parabola y² = 4ax lies in quadrants:

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I and II

III and IV

II and III

I and IV

The vertex of the parabola y² = 4ax is:

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(-a, 0)

(a, 0)

(0, -a)

(0, 0)

The focus of the parabola x2=-4ay is:

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(-a , 0)

(0, a)

(0, -a)

(a, 0)

Two circles of radius 3 cm and 4 cm touch each other externally. The distance between their centers is:

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1 cm

7cm

4cm

5cm

The conic is an ellipse, if:

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e = 1

e > 1

0 < e < 1

e = 0

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

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A pair of lines

Circle

Ellipse

Hyperbola

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