Question # 1

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

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

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

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

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Normal

Bisects

Equal to

None of these

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4a

2a

4b

2b

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

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x = a

x = -a

y = a

y = -a

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

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|CP| < r

|CP| = r

|CP| > r

None of these

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

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

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x² = 4ay

-x²= 4ay

-y²= 4ax

y²= 4ax

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

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x-axis

major axis

y-axis

minor axis

The point where the axis meets the parabola is called ________ of the parabola:

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Directrix

Vertex

Focus

Eccentricity

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

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

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x = 0

x = a

y = 0

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

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x = a

x = - a

y = a

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

An angle in a semi-circle is:

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0°

90°

180°

60°

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

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x-axis

y-axis

Major axis

Minor axis

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