Question # 1

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

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

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Tangent

Vertex

Axis

None

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(-6,4)

(-3,2)

(6,-4)

(3, -2)

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The vertex of the equation y² = 4ax is:

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(2, -2)

(1,1)

(0 , 0)

(2 , 2)

Equation of normal to the circle x2 + y2 =25 at (5cosθ,5sinθ)

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xcosθ+ysinθ =5

xcosθ -ysinθ =0

xsinθ -ycosθ =0

None of these

The equation of the circle with centre (-h, -k) and radius r is

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(x +h)²+ (y+k)²= r²

(x +h)²+ (y-k)²= r²

(x -h)²+ (y+k)²= r²

(x -h)²+ (y-k)²= r²

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 equation of vertical asymptotes of y = cos ecx is

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x = 0

y = 0

x =∞

y =∞

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

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

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Circle

Hyperbola

Ellipse

Pair of straight lines

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6

20

0

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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 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

The equation of the circle with centre (h, k) and radius r is

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(x+ h)²+ (y+ k)²= r²

(x+ h)²+ (y - k)²= r²

(x - h)²+ (y+ k)²= r²

(x - h)²+ (y - k)²= r²

Equation of parabola with focus F(-3,1) directrix x=3 is

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(y -1)2 =-12x

(y-1)2 =4x

(x+3)2 =4a(y-1)

y2 =-12(x-1)

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

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

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axis

focal chord

tangent

latus rectum

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

If t is the parameter for one end of a focal chord of the parabola y²= 4ax, then its length is

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The eccentricity of parabola is:

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1

0

Greater than 1

Less than 1

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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

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The point where the axis meets the parabola is called

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Directrix

Foucu

Chord

Vertix

The equation of the chord of the circle x²+ y²- 4x = 0 whose mid-point is (1, 0) is

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y = 2

y = 1

x = 2

x = 1

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2 b

2 a

2 ab

a + b

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184

none of these

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