Question # 1

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

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

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Outside

Inside

On

None of these

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

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If the cutting plane is slightly tillted and cuts only one nappe of the cone, then the section is a / an:

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Ellipse

Circular cone

Circle

Point circle

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

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Outside

Inside

On

None of these

The center of circle x² + y² + 2gx + 2fy + c = 0 is:

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(-g, -f)

(-f, -g)

(0, 0)

(g, f)

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

Two real and distinct 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

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

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Left

Upward

Right

Downward

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

The vertex of the parabola y² = -4ax is:

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(-a, 0)

(a, 0)

(0, -a)

(0, 0)

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

The conic is a parabola, if:

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e = 1

e > 1

0 < e < 1

e = 0

The parabola y² = 4ax lies in quadrants:

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I and II

III and IV

II and III

I and IV

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

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

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Straight line

Tangent line

Normal line

Vertical line

The opening of the parabola x²= 16y is to __________ of the x-axis:

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Left

Upward

Right

Downward

If the equation of the parabola is x² = 4ay, then opening of the parabola is to _______ of the x-axis:

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Left

Upward

Right

Downward

The equ. of directrix of the parabola y² = -4ax is:

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x = a

x = - a

y = a

y = -a

If a point lies inside a circle, then its distance from the center is:

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Equal to the radius

Less then the radius

Greater then the radius

Equal to or greater than the

The number e denotes the _______ of the conic:

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Directrix

Vertex

Focus

Eccentricity

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