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 A line segment whose end points lie on a circle is called The secant of the circle The arc of the circle The chord of the circle The circumference of the circle
2 The equation of the normal to the circle x2+ y2= 25 at (4, 3) is 3x - 4y =0 3x - 4y =5 4x + 3y = 5 4x + 3y = 25
3 The point (x1, y1) lies outside the circle x2+ y2+ 2gx + 2fy + c =0 if
4 The circle (x - 2)2+ (y + 3)2= 4 is not concentric with the circle (x - 2)<sup>2</sup>+ (y + 3)<sup>2</sup>= 9 (x + 2)<sup>2</sup>+ (y - 3)<sup>2</sup>= 4 (x + 2)<sup>2</sup>+ (y - 3)<sup>2</sup>= 8 (x - 2)<sup>2</sup>+ (y + 3)<sup>2</sup>= 5
5 If x + y + 1 = 0 touches the parabola y2=λx, thenλis equal to 2 4 6 8
6 The parabola y2= x is symmetric about x-axis y-axis Both x and y-axis The line y = x
7 If (a, b) is the mid-point of a chord passing thro' the vertex of the parabola y2= 4x, then a = 2b 2a = b a<sup>2</sup>= 2b 2a = b<sup>2</sup>
8 If t is the parameter for one end of a focal chord of the parabola y2= 4ax, then its length is
9 The point on y2 = 4ax nearest to the focus has its abciassae equal to -a a a/2 0
10 The radius of the circle (x - 1)2+ (y + 3)2= 61 is 8 4 64 None of these
11
12 The constant distance of all points of the circle from its centre is called the Radius of the circle Secant of the circle Chord of the circle Diameter of the circle
13 If a cone is cut by a plane perpendicular to the axis of the cone, then the section is a Parabola Circle Hyperbola Ellipse
14 If the st. line 3x + 4y = K touches the circle x2+ y2- 10x = 0 then the value of K is -1 or 20 -10 or 40 -2 or 20 2 or 20
15 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
16 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 2x - 3y = 0 3x + 2y = 0 3x - 2y = 0
17 The line 3x - 4y = 0 Is a tangent to the circle x<sup>2</sup>+ y<sup>2</sup>= 25 Is a normal to the circle x<sup>2</sup>+ y<sup>2 </sup>=25 Does not meet the circle x<sup>2</sup>+ y<sup>2</sup>= 25 Does not pass thro' the origin
18 2 b 2 a 2 ab a + b
19 A circle is a limiting case of an ellipse whose eccentricity Tends to a Tends to b Tends to 0 Tends to a + b
20 An ellipse A parabola A circle A hyperbola
21 The latus rectum of the ellipse 5x2+ 9y2= 45 is 10 / 3 5 / 3 3 / 5 3 / 10
22 The equation ax2+ 2hxy + by2 +2gx + 2fy + c =0 represents an ellipse if
23 The slope of the normal at the point (at2, 2at) of the parabola y2= 4ax is 1/t t -t -1/t
24 The line y = 2 x + c is a tangent to the parabola y2= 16 x if c equals -2 -1 0 2
25 The equation of the parabola with directirx x = 2 and the axis y = 0 is y<sup>2</sup>= 8x y<sup>2</sup>= -8x y<sup>2</sup>= 4x y<sup>2</sup>= -4x
26 The equation of the directrix of the parabola x2= 4ay is x + a = 0 x - a = 0 y + a = 0 y - a = 0
27 The eccentricity of the parabola y2= -8x is -2 2 -1 1
28 The length of the tangent from (2, 1) to the circle x2+ y2+ 4y + 3 = 0 is
29 The equation of the chord of the circle x2+ y2- 4x = 0 whose mid-point is (1, 0) is y = 2 y = 1 x = 2 x = 1
30 The line Ax + By + C = 0 will touch the circle x2+ y2=λ when C<sup>2</sup>=<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);">λ</span>(A<sup>2</sup>+ B<sup>2</sup>) A<sup>2</sup>=<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);">λ</span>(A<sup>2</sup>+ C<sup>2</sup>) B<sup>2</sup>=<span style="font-family: &quot;Times New Roman&quot;; font-size: 24px; color: rgb(34, 34, 34); text-align: center; background-color: rgb(255, 255, 224);">λ</span>(A<sup>2</sup>+ C<sup>2</sup>) None of these
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