Question # 1

Two circles are said to be concentric if they have

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same radius

same chord

same centre

same diameter

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

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P is on the circle

P is inside the circle

P is outside the circle

none of these

The equation of the directrix of the parabola x²= 4ay is

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x + a = 0

x - a = 0

y + a = 0

y - a = 0

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

The parabolay2=4ax open up if

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a<0

a≠0

a>0

All are incorrect

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(g,f)

(-g,f)

(g,-f)

(-g,-f)

The vertices of the ellipse x²+ 4y²= 16 are

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The second degree equation 2x2 -xy+ 5x -2y +2 =0 represents

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Circle

Hyperbola

Ellipse

Pair of straight lines

A chord passing through the centre of the circle is called

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the secant of the circle

the tangent of the circle

the arc of the circle

the diameter of the circle

The tangent to the parabola y2 =4ax and perpendicular line from the focus on it meet

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x =0

y =0

x =-9

y = -a

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c = 0

c = -1

c = -2

c = 1

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The point on y²= 4ax nearest to the focus has its abciassae equal to

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-a

a

a/2

0

The second degree equation of the form Ax2 +By2 +Gx +Fy +C =0 represent hyperbola if

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A = B≠ 0

A≠ B and both are of same sign

A≠ B both are of opposite sign

Either A = 0 or B =0

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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none of these

The line y =mx +1 is tangent to the parabola y2 =4x if

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m=1

m=2

m=3

m=4

The eccentricity e of an ellipse is always

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Rational

Real

Irrational

Integer

The area of the circle centred at (1,2) and passing through (4,6) is

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30 πsq.units

5π sq.units

15π sq.units

25π sq.units

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none of these

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

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x = 0

y = 0

x = a

y = 0

The equation of the circle with centre origin and radius r is

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x²+ y²= 1

x²+ y²= r²

x²+ y²= 0

x²- y²= r²

The number of real tangents that can be drawn to the ellipse 3x²+ 5y²= 32 passing thro. (3, 5) is

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0

1

2

Infinite

If x + y + 1 = 0 touches the parabola y²=λx, thenλis equal to

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2

4

6

8

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184

none of these

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

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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)

A square is inscribed in the circle x²+ y²- 2x + 4y + 3 =0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is

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The two different parts of the hyperbola are called its

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Vertices

Directrices

Nappes

Branches

I f the focus is F ( 0,-a) and directrix is the line v=a, then equation of the parabola is:

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x² = 4ay

y² = 4ax

y² = -4ax

x² = 4ax

The equation of the normal to the circle x²+ y²= 25 at (4, 3) is

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3x - 4y =0

3x - 4y =5

4x + 3y = 5

4x + 3y = 25

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