Important Questions of Conic Section Mathematics | Zigya

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 Multiple Choice QuestionsMultiple Choice Questions

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411.

If the point of intersection of the tangents drawn at the points where the line 5x + y + 1 = 0 cuts the circle x2 + y2 - zx - 6y - 8 = 0 is (a, b), then 5a + b =

  • 3

  •  - 44

  •  - 1

  • 4


412.

If 2kx + 3y - 1 = 0, 2x + y + 5 = 0 are conjugate lines with respect to the circle x2 + y2 - 2x - 4y - 4 = 0, then k =

  • 3

  • 4

  • 1

  • 2


413.

The equations of the parabola whose axis is parallel to the X-axis and which passes through the points (- 2, 1), (1, 2)(- 1, 3) is

  • 18y2 - 12x - 21y - 21 = 0

  • 5y2 + 2x - 21y + 20 = 0

  • 15y2 + 12x - 11y + 20 = 0

  • 25y2 - 2x - 65y + 36 = 0


414.

The angle between the two circles, each passing through the centre of the other is

  • 2π3

  • π2

  • π6

  • π


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415.

If log13z2 - z + 12 + z > - 2, then z lies inside

  • a triangle

  • an ellipse

  • a circle

  • a square


416.

A circle having centre at the origin passes through the three vertices of an equilateral triangle the length of its median being 9 units. Then the equation of that circle is

  • x2 + y2 = 9

  • x2 + y2 = 18

  • x2 + y2 = 36

  • x2 + y2 = 81


417.

A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola x24 - y22 = 1  at the point (x1, y1). Then x12 + 5y12 is equal to :

  • 10

  • 5

  • 8

  • 6


 Multiple Choice QuestionsShort Answer Type

418.

The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x2 + y2 – 2x – 4y + 4 = 0 at two distinct points is .... 


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 Multiple Choice QuestionsMultiple Choice Questions

419.

For some θ  0, π2, if the eccentricity of the hyperbola, x2 - y2sec2θ = 10 is 5 times the eccentricity of the ellipse , x2sec2θ + y2 = 5, then the length of the latus rectum of the ellipse, is

  • 253

  • 26

  • 453

  • 30


420.

The area (in sq. units) of an equilateral triangle inscribed in the parabola y2 = 8x, with one of its vertices on the vertex of this parabola is

  • 643

  • 1923

  • 1283

  • 2563


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