Question # 1

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

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32

16

18

8

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

y² =4ax, is:

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2a

a

x + a

x-a

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5

25

3

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 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 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 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

The line joining the center of a circle to the midpoint of the chord is

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Perpendicular to the tnagent

Perpendicular to the normal

Perpendicular to the chord

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

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 parabola y²= x is symmetric about

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x-axis

y-axis

Both x and y-axis

The line y = x

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

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Circle

Ellipse

Parabola

Hyoerbola

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c = 0

c = -1

c = -2

c = 1

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 equation x2+ y2- 8x+ 6y+ 25= 0 represents

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A circle

A pair of straight lines

A point

None of these

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The conic is a parabola if

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e < 1

e > 1

e = 1

None of these

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8

4

64

the curve of the parabola y² = -4ax is symmetric with respect to

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x -axis

y - axis

Botha x and y- axis

None of thes

Conic sections or simply conics are the curves obtained by cutting a right circular cone by

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a line

two lines

a plane

two planes

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11

61

1

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

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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 equation of vertical asymptotes of y = cos ecx is

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x = 0

y = 0

x =∞

y =∞

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6

20

0

The line y = 2 x + c is a tangent to the parabola y²= 16 x if c equals

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-2

-1

0

2

The directrix of y2 =-4ax is

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y =-a

y = a

x = a

x = -a

The general equation of a circle is

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