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

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

• Circle A
• Ellipse B
• Parabola C
• Hyoerbola D

If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve obtained is

• an ellipse A
• a hyperbola B
• a 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 x²+ y²= 0 represents

• A circle A
• A degenerate circle B
• An empty set C
• A st. line D

• 
  A
• 
  B
• 
  C
• none of these 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

• 2 b A
• 2 a B
• 2 ab C
• a + b D

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

• Hyperbola A
• Parabolas B
• Ellipses C
• None of these D

• 
  A
• 
  B
• 
  C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D

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

The conic is a parabola, when:

• ᵨ > 1 A
• ᵨ < 1 B
• ᵨ = 1 C
• ᵨ = 0 D

The eccentricity of parabola is:

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

If (2,0) is the vertex and y-axis is directrix of parabola then focus is

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

• 
  A
• 
  B
• 
  C
• 
  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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If the st. line 3x + 4y = K touches the circle x²+ y²- 10x = 0 then the value of K is

• -1 or 20 A
• -10 or 40 B
• -2 or 20 C
• 2 or 20 D

• 
  A
• 
  B
• 
  C
• 
  D

If the vertex of the parabola is the origin and directrix is x+5 = 0 . then its latus rectum is:

• 10 A
• 5 B
• 0 C
• 20 D

• 
  A
• 
  B
• 
  C
• 
  D

For what value of k, 3x -2y+ k= 0 is tangent to the circle x2 +y2 +6x -4y =0

• k=0 A
• k=0 or 26 B
• k = 26 C
• k=-13 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

The span of a standard parabola depends upon

• x A
• a B
• y C
• y2 D

The line y =mx +1 is tangent to the parabola y2 =4x if

• m=1 A
• m=2 B
• m=3 C
• m=4 D

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

The circle (x - 2)²+ (y + 3)²= 4 is not concentric with the circle

• (x - 2)²+ (y + 3)²= 9 A
• (x + 2)²+ (y - 3)²= 4 B
• (x + 2)²+ (y - 3)²= 8 C
• (x - 2)²+ (y + 3)²= 5 D