ECAT Pre General Science Chapter 23 MCQ Test With Answer for Mathematics chapter 23 (Conic Sections)

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

• 
  A
• 
  B
• 
  C
• 
  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 number of standard parabolic functions are is

• 4 A
• 2 B
• 3 C
• 1 D

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

• 32 A
• 16 B
• 18 C
• 8 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The perpendicular bisector of any chord of a circle

• Passes through the centre of the circle A
• Does not pass through the centre of the circle B
• May or may not pass through the centre of the circle C
• None of these 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

The common point to four standard parabolas

• Focus A
• Centre B
• Vertex C
• P(x,y) D

The eccentricity e of an ellipse is always

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

• 
  A
• 
  B
• 
  C
• 
  D

The point which is closet to the focus of a parabola is:

• vertex A
• Chord B
• Focus C
• Directix D

Two circles x2 +y2 +8x -9= 0 and x2+y2+6y +k =0 touchinternallyif the value of k is

• k = 9 A
• k = ±9 B
• k=-9 C
• k=11 D

The equation of the tangent at vertex to the parabola is y2 = -8(x -3)

• y=0 A
• x=3 B
• x=1 C
• x=5 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• xcosθ+ysinθ =5 A
• xcosθ -ysinθ =0 B
• xsinθ -ycosθ =0 C
• None of these D

The line y = 4x + c touches the hyperbola x²- y²= 1 if

• 
  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

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

• x -axis A
• y - axis B
• Botha x and y- axis C
• None of thes D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If (a, b) is the mid-point of a chord passing thro' the vertex of the parabola y²= 4x, then

• a = 2b A
• 2a = b B
• a²= 2b C
• 2a = b² D

• 
  A
• 
  B
• 
  C
• 
  D

The second degree equation of the form Ax2 +By2 +Gx +Fy +C =0 represent hyperbola if

• A = B≠ 0 A
• A≠ B and both are of same sign B
• A≠ B both are of opposite sign C
• Either A = 0 or B =0 D

The lotus of intersection of perpendicular tangents to the parabola y² = 4ax is:

• Axis of the parabola A
• Focal chord of the parabos B
• The tangent at vertex of the parabola C
• a directrix of the parabola D

The end points of the major axis of the ellipse are called its

• Foci A
• Vertices B
• Co - vertices C
• None of these D

• 6 A
• 
  B
• 20 C
• 0 D

The eccentricity of parabola is:

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

The centre of the conic x2 +16x +4y2 -16y +76 =0 is

• (0,10) A
• (-8,4) B
• (-8,-2) C
• (1,1) D