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

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x = a

x = -a

y = a

y = -a

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

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

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(1, -2)

(0, 1)

(-1, -2)

(1, 2)

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

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

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

the focal chord perpendicular to the axis of the parabola is called _____________ of the parabola:

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Directrix

Latus rectum

Focus

Focal chord

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

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None

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

If equation of circle is (x - h)² + (y - k)² = r², then center of a circle:

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(-h, -k)

(h, k)

(-h, k)

(h, -k)

If a circle and a line intersect in two points, then the line is called:

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A chord

A secant

A diameter

None of these

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 graph of the parabola x² = -4ay is symmetric about:

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x-axis

major axis

y-axis

minor axis

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

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(a, 0)

(0, 0)

(0, -a)

(0, a)

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 graph of the parabola y² = -4ax is symmetric about:

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x-axis

major axis

y-axis

minor axis

The focus of the parabola x² = 4ay:

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(0, a)

(-a , 0)

(0, -a)

(a, 0)

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

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

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x = X - h

x = X + h

x + X = h

None

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a

2b

b

2a

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