Question # 1

The eccentricity of the conic 9x²- 16y²= 144 is

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4/5

5/4

4/3

3/4

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

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Chord

Tangent

Lust rectum

directrix

The number of tangents to the circle x2+ y2 -8x -6y +9 =0 which pass through the point (3,-2) is

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2

1

0

None of these

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

x =r cosθ,y= sinθ are the parametric equations of

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Circle

Ellipse

Parabola

Hyoerbola

If (a, b) is the mid-point of a chord passing thro' the vertex of the parabola y²= 4x, then

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a = 2b

2a = b

a²= 2b

2a = b²

If e,e′ be the eccentricities of two conics S=0 and S′ =0 and if e2 +e′2 =3 then both S and S′ can be

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Hyperbola

Parabolas

Ellipses

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

a chord passing through the focus of a parabola is called a:

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Focal chord

Latus rectum

Tangent

Directrix

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2 b

2 a

2 ab

a + b

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

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(-6,4)

(-3,2)

(6,-4)

(3, -2)

The vertex of the parabola (xsin a -ycos a)2 =4a(xcos a +ysin a) lies at

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(acos a,asin a)

(a,0)

(cos a,sin a)

(0,0)

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

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y=0

x=3

x=1

x=5

A line joining two distinct points on a parabola is called

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Axis

Directrix

Chord

Tangent

If the cutting plane is slightly tilted and cuts only one nappe of the cone, the intersection is

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an ellipse

a hyperbola

a circle

a parabola

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A parabola

An ellipse

A hyperbola

A circle

The equation of the parabola with directirx x = 2 and the axis y = 0 is

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y²= 8x

y²= -8x

y²= 4x

y²= -4x

The parametric equations of a circle are

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For the parabola the line through focus and perpendicular to the directrix is called

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Tangent

Vertex

Axis

None

The general equation of a circle is

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(1, 3)

(-1, -3)

(1, -3)

(-1, 3)

If the distance of any point on the curve from any of the two lines approaches zero then it is called

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Axis

Directrices

Asymptotes

None

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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

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

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