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 The eccentricity e of an ellipse is always Rational Real Irrational Integer
2 The line y= 4x +c touches the hyperbola x2- y2 =1 if and only if c =±√2 c =0 c=±√17 c=±√15
3 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
4 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)
5 If eccentricity of ellipse becomes zero then it takes the form of A parabola A circle A straight line None of these
6 The sum of the focal distance from any point on the ellipse 9x2 +16y2 =144 is 32 16 18 8
7 The centre of the conic x2 +16x +4y2 -16y +76 =0 is (0,10) (-8,4) (-8,-2) (1,1)
8 Intersection of two parabolas parabola Two points Four points Hyperobla
9 If either A = 0 or B =0,then Ax2 +By2 +2Gx +2Fy +c =0 represents a Circle Hyperbola Ellipse Parabola
10 ax2 +2hxy +by2 +2gx +2fy +c =0 may represent an ellipse if h2 -ab <0 h2 -ab≠ 0 h2 -ab =0 h2 -ab >0
11 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°
12 The second degree equation 2x2 -xy+ 5x -2y +2 =0 represents Circle Hyperbola Ellipse Pair of straight lines
13 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
14 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
15 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
16 The slope of the tangent at the point (h,h) of the circle x2 +y2 =a2 is 0 1 -1 h
17 The equation x2+ y2- 8x+ 6y+ 25= 0 represents A circle A pair of straight lines A point None of these
18 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
19 The tangent to the parabola y2 =4ax and perpendicular line from the focus on it meet x =0 y =0 x =-9 y = -a
20 If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____ 12 8 24 -24
21 The line y =mx +1 is tangent to the parabola y2 =4x if m=1 m=2 m=3 m=4
22 If (2,0) is the vertex and y-axis is directrix of parabola then focus is (2,0) (-2,0) (4,0) (-4,0)
23 Number of conics is 1 3 2 4
24 The vertex of the parabola (xsin a -ycos a)2 =4a(xcos a +ysin a) lies at (acos a,asin a) (a,0) (cos a,sin a) (0,0)
25 The number of standard parabolic functions are is 4 2 3 1
26 The parabolay2=4ax open up if a<0 a≠0 a>0 All are incorrect
27 y=-a is the equation of the directrix of y2 =4ax x2=-4ay x2=4ay y2=-4ax
28 Equation of normal to the circle x2 + y2 =25 at (5cosθ,5sinθ) xcosθ+ysinθ =5 xcosθ -ysinθ =0 xsinθ -ycosθ =0 None of these
29 For what value of k, 3x -2y+ k= 0 is tangent to the circle x2 +y2 +6x -4y =0 k=0 k=0 or 26 k = 26 k=-13
30 Two circles x2 +y2 +8x -9= 0 and x2+y2+6y +k =0 touchinternallyif the value of k is k = 9 k = ±9 k=-9 k=11
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