Question # 1

The equation ax²+ 2hxy + by²+2gx + 2fy + c =0 represents an ellipse if

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The line 2x +√6y =2 is a tangent to the curve x2 -2y2 =4 The point of contact is

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(√6,1)

(2,3)

(7,-2√6)

(4,-√6)

If (0, 0) and (1, 0) are the end points of a diameter, then the equation of the circle is

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none of these

A line joining two distinct points on a parabola is called a ______ of the parabola.

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Chord

Tangent

Lust rectum

directrix

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Coordinates of the focus of the parabola x² - 4x -8y-4=0 are:

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(0,2)

(,0,1)

(2,0)

(1,2)

The equation of the circle with centre (h, k) and radius r is

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(x+ h)²+ (y+ k)²= r²

(x+ h)²+ (y - k)²= r²

(x - h)²+ (y+ k)²= r²

(x - h)²+ (y - k)²= r²

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none of these

The slope of the tangent at the point (h,h) of the circle x2 +y2 =a2 is

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0

1

-1

h

Which shape of the following objects are approximately parabolic ares?

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Light reflectors

Force

Weight of the pendul

None of these

The equation of the chord of the circle x²+ y²- 4x = 0 whose mid-point is (1, 0) is

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y = 2

y = 1

x = 2

x = 1

The centre fo the circle x²+ y²+ 12x -10 = 0 is

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(12, -10)

(6, -5)

(-12, 10)

(-6, 5)

The line Ax + By + C = 0 will touch the circle x²+ y²=λ when

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C²=λ(A²+ B²)

A²=λ(A²+ C²)

B²=λ(A²+ C²)

None of these

The point which is closet to the focus of a parabola is:

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vertex

Chord

Focus

Directix

What is the axis of the parabola y²= 4ax?

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x = 0

y = 0

x = a

y = 0

If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a

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parabola

circle

hyperbola

ellipse

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The equation of the circle wit (-1, 1) and radius 2 is

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A line segment whose end points lie on a circle is called

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the secant of the circle

the arc of the circle

the chord of the circle

the circumference of the circle

Area of the circle with ends of a diameter at (-3,2) and (5,-6)

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128π sq. units

64π sq. units

32π sq.units

None of these

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none of these

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

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an ellipse

a hyperbola

a circle

a parabola

The tangents drawn from the point P to a circle are real and distinct if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

The lotus of intersection of perpendicular tangents to the parabola y² = 4ax is:

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Axis of the parabola

Focal chord of the parabos

The tangent at vertex of the parabola

a directrix of the parabola

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If the st. line 3x + 4y = K touches the circle x²+ y²- 10x = 0 then the value of K is

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-1 or 20

-10 or 40

-2 or 20

2 or 20

If (2, 3) and (2, 5) are end points of a diameter of a circle, then the centre of the circle is

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(2, 4)

(4, 8)

(0, 2)

(0, -2)

The line y = 2 x + c is a tangent to the parabola y²= 16 x if c equals

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-2

-1

0

2

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