Question # 1

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An ellipse

A parabola

A circle

A hyperbola

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

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The remove the term involving xy, from 7x2 -6√3xy+ 13y2 -16 =0 the angel of rotation is

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θ = 30°

θ = 45°

θ = 60°

θ = 75°

The line 3x - 4y = 0

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Is a tangent to the circle x²+ y²= 25

Is a normal to the circle x²+ y²=25

Does not meet the circle x²+ y²= 25

Does not pass thro' the origin

The directrix of y2 =-4ax is

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y =-a

y = a

x = a

x = -a

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

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The sum of the focal distance from any point on the ellipse 9x2 +16y2 =144 is

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32

16

18

8

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The constant distance of all points of the circle from its centre is called the

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radius of the circle

secant of the circle

chord of the circle

diameter of the circle

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0

1

13

The conic ax2+2hxy+by2+2gx+2fy+c= 0 never represent a circle if

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a≠ b,h≠0

a=b

h≠0

h=0

The ellipse and hyperbola are called

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Concentric conics

Central conics

Both a b

None

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

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The locus of the centre of a circle which touches two given circles externally is:

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a hyperbola

an ellipse

a circle

a parabola

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 distance of point P(x,y) from focus in a parabola

y² =4ax, is:

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2a

a

x + a

x-a

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

A circle is a limiting case of an ellipse whose eccentricity

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Tends to a

Tends to b

Tends to 0

Tends to a + b

y=0 of the parabola y² = 4ax is the

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equation of directirx

Equatio of the tangent

Equation of axis

equation of latus rectum

Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is

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(2, 0)

(3, 0)

(0, 3)

(3, 2)

The axis of the parabola x² = 4ay is:

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y = 0

x = 0

x = -a

y = a

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

Two circles x2 +y2 +8x -9= 0 and x2+y2+6y +k =0 touchinternallyif the value of k is

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k = 9

k = ±9

k=-9

k=11

The centre of the circle x2+y2 -2fx-2gy+x=0 is

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(-g,-f)

(g,f)

(f,g)

(-f,-g)

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 equation of the tangent at vertex to the parabola is y2 = -8(x -3)

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y=0

x=3

x=1

x=5

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none of these

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

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2

4

6

8

If either A = 0 or B =0,then Ax2 +By2 +2Gx +2Fy +c =0 represents a

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Circle

Hyperbola

Ellipse

Parabola

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