ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test With Answers

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ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test

Sr. # Questions Answers Choice
1 If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a parabola circle hyperbola ellipse
2 Conic sections or simply conics are the curves obtained by cutting a right circular cone by a line two lines a plane two planes
3 The second degree equation of the form Ax2 +By2 +Gx +Fy +C =0 represent hyperbola if A = B≠ 0 A≠ B and both are of same sign A≠ B both are of opposite sign Either A = 0 or B =0
4 If the distance of any point on the curve from any of the two lines approaches zero then it is called Axis Directrices Asymptotes None
5 The ellipse and hyperbola are called Concentric conics Central conics Both a b None
6 The directrix of y2 =-4ax is y =-a y = a x = a x = -a
7 A line joining two distinct points on a parabola is called Axis Directrix Chord Tangent
8 For the parabola the line through focus and perpendicular to the directrix is called Tangent Vertex Axis None
9 The eccentricity e of an ellipse is always Rational Real Irrational Integer
10 The line y= 4x +c touches the hyperbola x2- y2 =1 if and only if c =±√2 c =0 c=±√17 c=±√15
11 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 Parabolas Ellipses None of these
12 The line 2x +√6y =2 is a tangent to the curve x2 -2y2 =4 The point of contact is (√6,1) (2,3) (7,-2√6) (4,-√6)
13 If eccentricity of ellipse becomes zero then it takes the form of A parabola A circle A straight line None of these
14 The sum of the focal distance from any point on the ellipse 9x2 +16y2 =144 is 32 16 18 8
15 The centre of the conic x2 +16x +4y2 -16y +76 =0 is (0,10) (-8,4) (-8,-2) (1,1)
16 Intersection of two parabolas parabola Two points Four points Hyperobla
17 If either A = 0 or B =0,then Ax2 +By2 +2Gx +2Fy +c =0 represents a Circle Hyperbola Ellipse Parabola
18 ax2 +2hxy +by2 +2gx +2fy +c =0 may represent an ellipse if h2 -ab <0 h2 -ab≠ 0 h2 -ab =0 h2 -ab >0
19 The remove the term involving xy, from 7x2 -6√3xy+ 13y2 -16 =0 the angel of rotation is θ = 30° θ = 45° θ = 60° θ = 75°
20 The second degree equation 2x2 -xy+ 5x -2y +2 =0 represents Circle Hyperbola Ellipse Pair of straight lines
21 If the line 2x -y +k =0 is a diameter of the circle x2 +y2 +6x -6y +5 =0 then k is equal to 12 9 6 3
22 The area of the circle centred at (1,2) and passing through (4,6) is 30 πsq.units 5π sq.units 15π sq.units 25π sq.units
23 The number of tangents to the circle x2+ y2 -8x -6y +9 =0 which pass through the point (3,-2) is 2 1 0 None of these
24 The slope of the tangent at the point (h,h) of the circle x2 +y2 =a2 is 0 1 -1 h
25 The equation x2+ y2- 8x+ 6y+ 25= 0 represents A circle A pair of straight lines A point None of these
26 Two circle s1: x2+ y2 +2x- 2y- 7= 0: s2: x2+ y2- 6x+ 4y+ 9= 0 Touch externally Touch internally Intersects each other Do not intersects
27 The tangent to the parabola y2 =4ax and perpendicular line from the focus on it meet x =0 y =0 x =-9 y = -a
28 If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____ 12 8 24 -24
29 The line y =mx +1 is tangent to the parabola y2 =4x if m=1 m=2 m=3 m=4
30 If (2,0) is the vertex and y-axis is directrix of parabola then focus is (2,0) (-2,0) (4,0) (-4,0)
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