Question # 1

Equation of the chord of contact to the tangents drawn from (-3,4) to the circle x2 + y2 = 21

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-3x + 4y =21

4x - 3x = 0

-3x + 4y = 25

None of these

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 circle (x - 2)²+ (y + 3)²= 4 is not concentric with the circle

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(x - 2)²+ (y + 3)²= 9

(x + 2)²+ (y - 3)²= 4

(x + 2)²+ (y - 3)²= 8

(x - 2)²+ (y + 3)²= 5

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184

none of these

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5

25

3

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

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2

4

6

8

The fixed point from which all the points of a circle are equidistant is called the

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chord of the circle

centre of the circle

diameter of the circle

radius of the circle

If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____

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12

8

24

-24

If (x₁, y₁) and (x₂,y₂) are the end points of a diameter then the centre of the circle is

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Which shape of the following objects are approximately parabolic ares?

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Light reflectors

Force

Weight of the pendul

None of these

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

The equation of a line parallel to the tangent to the circle x²+ y²= 16 at the point (2, 3) and passing thro' the origin is

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2x + 3y = 0

2x - 3y = 0

3x + 2y = 0

3x - 2y = 0

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

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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 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)

The conic is a parabola if

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e < 1

e > 1

e = 1

None of these

The conic is a parabola, when:

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ᵨ > 1

ᵨ < 1

ᵨ = 1

ᵨ = 0

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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

The parabolay2=4ax open up if

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a<0

a≠0

a>0

All are incorrect

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)

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

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Chord

Tangent

Lust rectum

directrix

Two circle s1: x2+ y2 +2x- 2y- 7= 0: s2: x2+ y2- 6x+ 4y+ 9= 0

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Touch externally

Touch internally

Intersects each other

Do not intersects

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y=-a is the equation of the directrix of

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y2 =4ax

x2=-4ay

x2=4ay

y2=-4ax

Ifᵨ> 1 , then the conic, is:

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Ellipse

Parabola

Hyperbola

None of these

A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. Then CP²+ CQ²+ CR²+ CS²=

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r²

2 r²

3 r²

4 r²

The common point to four standard parabolas

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Focus

Centre

Vertex

P(x,y)

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