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 slope of the normal at the point (at2, 2at) of the parabola y2= 4ax is 1/t t -t -1/t
2 The line y = 2 x + c is a tangent to the parabola y2= 16 x if c equals -2 -1 0 2
3 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
4 The equation of the directrix of the parabola x2= 4ay is x + a = 0 x - a = 0 y + a = 0 y - a = 0
5 The eccentricity of the parabola y2= -8x is -2 2 -1 1
6 The length of the tangent from (2, 1) to the circle x2+ y2+ 4y + 3 = 0 is
7 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
8 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
9 Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is (2, 0) (3, 0) (0, 3) (3, 2)
10 The equation x2+ y2= 0 represents A circle A degenerate circle An empty set A st. line
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12 1 5 7 9
13 A parabola An ellipse A hyperbola A circle
14 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= r<sup>2</sup> 2 r<sup>2</sup> 3 r<sup>2</sup> 4 r<sup>2</sup>
15
16 The line y = 4x + c touches the hyperbola x2- y2= 1 if
17 The eccentricity of the conic 9x2- 16y2= 144 is 4/5 5/4 4/3 3/4
18 A chord passing through the centre of the circle is called the secant of the circle the tangent of the circle the arc of the circle the diameter of the circle
19 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
20 6 20 0
21 184 none of these
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30 none of these
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