ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test

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

• A circle A
• A pair of straight lines B
• A point C
• None of these D

• 6 A
• 
  B
• 20 C
• 0 D

The tangents drawn from the point P to a circle are real and distinct if

• P is on the circle A
• P is inside the circle B
• P is outside the circle C
• none of these D

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

• 2 A
• 4 B
• 6 C
• 8 D

• 
  A
• 
  B
• 
  C
• 
  D

the latus rectum of the parabola x³ = -4ay is:

• x = a A
• y = -a B
• x = -a C
• y = 0 D

The eccentricity of parabola is:

• 1 A
• 0 B
• Greater than 1 C
• Less than 1 D

The equation of the directrix of the parabola x²= 4ay is

• x + a = 0 A
• x - a = 0 B
• y + a = 0 C
• y - a = 0 D

• 
  A
• 
  B
• 
  C
• 
  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

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

• 0 A
• 1 B
• 13 C
• 
  D

What is the axis of the parabola y² = 4ax?

• x = 0 A
• y = 0 B
• x = a C
• y = 0 D

• 
  A
• 
  B
• 
  C
• none of these D

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

• 
  A
• 
  B
• 
  C
• 
  D

Latus rectum = 4 x ______________

• focal distance of the vertex A
• Chord B
• Focus C
• 1/2 D

The constant distance of all points of the circle from its centre is called the

• radius of the circle A
• secant of the circle B
• chord of the circle C
• diameter of the circle D

The ellipse and hyperbola are called

• Concentric conics A
• Central conics B
• Both a b C
• None 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

The parabola y²= x is symmetric about

• x-axis A
• y-axis B
• Both x and y-axis C
• The line y = x D

The line Ax + By + C = 0 will touch the circle x²+ y²=λ when

• C²=λ(A²+ B²) A
• A²=λ(A²+ C²) B
• B²=λ(A²+ C²) C
• None of these D

The two different parts of the hyperbola are called its

• Vertices A
• Directrices B
• Nappes C
• Branches D

• 
  A
• 
  B
• 
  C
• 
  D

The slope of the normal at the point (at², 2at) of the parabola y²= 4ax is

• 1/t A
• t B
• -t C
• -1/t D

If a plane passes through the vertex of a cone then the intersection is

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

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=

• r² A
• 2 r² B
• 3 r² C
• 4 r² D

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

• 2x + 3y = 0 A
• 2x - 3y = 0 B
• 3x + 2y = 0 C
• 3x - 2y = 0 D

The parabolay2=4ax open up if

• a<0 A
• a≠0 B
• a>0 C
• All are incorrect D

A circle is a limiting case of an ellipse whose eccentricity

• Tends to a A
• Tends to b B
• Tends to 0 C
• Tends to a + b D

A square is inscribed in the circle x²+ y²- 2x + 4y + 3 =0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is

• 
  A
• 
  B
• 
  C
• 
  D