Question # 1

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

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-a

a

a/2

0

For what value of k, 3x -2y+ k= 0 is tangent to the circle x2 +y2 +6x -4y =0

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k=0

k=0 or 26

k = 26

k=-13

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An ellipse

A parabola

A circle

A hyperbola

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

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)

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

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 eccentricity of parabola is:

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1

0

Greater than 1

Less than 1

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

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Circle

Ellipse

Parabola

Hyoerbola

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 axis of the parabola x² = 4ay is:

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y = 0

x = 0

x = -a

y = a

The general equation of a circle is

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An ellipse slides between two lines at right angles to one another. The locus of its centre is :

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a parabola

an ellipse

a circle

a hyperbola

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

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Circle

Hyperbola

Ellipse

Pair of straight lines

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 point (x₁, y₁) lies outside the circle x²+ y²+ 2gx + 2fy + c =0 if

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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 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

ax2 +2hxy +by2 +2gx +2fy +c =0 may represent an ellipse if

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h2 -ab <0

h2 -ab≠ 0

h2 -ab =0

h2 -ab >0

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 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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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 vertex of the equation y² = 4ax is:

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(2, -2)

(1,1)

(0 , 0)

(2 , 2)

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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

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

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The equation of vertical asymptotes of y = cos ecx is

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x = 0

y = 0

x =∞

y =∞

If a > 0 they parabola y2 =-4ax lies in

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I and iv quadrant

I quadrant

II and III quadrant

All are incorrect

The line through the focus and perpendicular to the directrix is called ______ of the parabola

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axis

focal chord

tangent

latus rectum

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