ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test

The equation of the circle wit (-1, 1) and radius 2 is

• 
  A
• 
  B
• 
  C
• 
  D

Co-ordinate of a point on the parabola y² = 8x whose focal distance is 4 are:

• (2 , 4) A
• (-2 ,-4) B
• (-2, 4) C
• (2,-4) D

A chord passing through the centre of the circle is called

• the secant of the circle A
• the tangent of the circle B
• the arc of the circle C
• the diameter of the circle D

• An ellipse A
• A parabola B
• A circle C
• A hyperbola D

The eccentricity e of an ellipse is always

• Rational A
• Real B
• Irrational C
• Integer D

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

• a parabola A
• an ellipse B
• a circle C
• a hyperbola D

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

• (x+ h)²+ (y+ k)²= r² A
• (x+ h)²+ (y - k)²= r² B
• (x - h)²+ (y+ k)²= r² C
• (x - h)²+ (y - k)²= r² D

A line segment whose end points lie on a circle is called

• The secant of the circle A
• The arc of the circle B
• The chord of the circle C
• The circumference of the circle D

• 
  A
• 
  B
• 
  C
• none of these D

The line 3x - 4y = 0

• Is a tangent to the circle x²+ y²= 25 A
• Is a normal to the circle x²+ y² =25 B
• Does not meet the circle x²+ y²= 25 C
• Does not pass thro' the origin D

• 
  A
• 
  B
• 
  C
• 
  D

The equation of the circle with centre (5, -2) and radius 4 is

• (x-5)²+ (y+2)²= 16 A
• (x-5)²+ (y+2)²= 4 B
• (x-5)²+ (y-2)²= 16 C
• (x-5)²+ (y-2)²= 4 D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• -2 A
• -1 B
• 0 C
• 2 D

Number of conics is

• 1 A
• 3 B
• 2 C
• 4 D

• 
  A
• 
  B
• 
  C
• none of these D

• (1, 3) A
• (-1, -3) B
• (1, -3) C
• (-1, 3) D

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

• (y -1)2 =-12x A
• (y-1)2 =4x B
• (x+3)2 =4a(y-1) C
• y2 =-12(x-1) D

The remove the term involving xy, from 7x2 -6√3xy+ 13y2 -16 =0 the angel of rotation is

• θ = 30° A
• θ = 45° B
• θ = 60° C
• θ = 75° D

The line 2x +√6y =2 is a tangent to the curve x2 -2y2 =4 The point of contact is

• (√6,1) A
• (2,3) B
• (7,-2√6) C
• (4,-√6) D

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

• a line A
• two lines B
• a plane C
• two planes D

The equation of the normal to the circle x²+ y²= 25 at (4, 3) is

• 3x - 4y =0 A
• 3x - 4y =5 B
• 4x + 3y = 5 C
• 4x + 3y = 25 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• Tangent A
• Vertex B
• Axis C
• None D

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

• 
  A
• 
  B
• 
  C
• 
  D

The straight line passing through the focus and perpendicular to the directrix of the conic is known as its

• Tangent A
• axis B
• Focal chord C
• major or manor axis D

The length of the tangent from (2, 1) to the circle x²+ y²+ 4y + 3 = 0 is

• 
  A
• 
  B
• 
  C
• 
  D

Two circles are said to be concentric if they have

• same radius A
• same chord B
• same centre C
• same diameter D

• 8 A
• 
  B
• 4 C
• 64 D

• c = 0 A
• c = -1 B
• c = -2 C
• c = 1 D