Important Questions of Conic Section Mathematics | Zigya

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381.

A hyperbola passing through a focus of the  ellipsex2169 + y225 = 1. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse. The product of eccentricities is 1. Then, the equation of the hyperbola is

  • x2144 - y29 = 1

  • x2169 - y225 = 1

  • x2144 - y225 = 1

  • x2125 - y29 = 1


382.

If the curves x2a2 + y2b2 = 1 and x225 + y216 = 1 cut each other orthogonally, then a2 - b2 = ? 

  • 9

  • 400

  • 75

  • 41


383.

Te area (m sq units) of the region bounded by x = -1, x = 2, y = x2 + 1 and y = 2x - 2 is

  • 10

  • 7

  • 8

  • 9


384.

The sum of the minimum and maximum distance of the point (4, - 3) to the circle x2 + y2 + 4x - 10y - 7 = 0, is

  • 10

  • 12

  • 16

  • 20


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385.

The locus of centres of the circles, which cut the circles x2 + y2 + 4x - 6y + 9 and x2 + y2 - 5x + 4y + 2 = 0 orthogonally, is

  • 3x + 4y - 5 = 0

  • 9x - 10y + 7 = 0

  • 9x + 10y - 7 = 0

  • 9x - 10y + 11 = 0


386.

If x - y + 1 = 0 meets the circle x2 + y2 + y - 1 = 0 at A and B, then the equation of the circle with AB as diameter is

  • 2(x2 + y2) + 3x - y + 1 = 0

  • 2(x2 + y2) + 3x - y + 2 = 0

  • 2(x2 + y2) + 3x - y + 3 = 0

  • x2 + y2 + 3x - y + 4 = 0


387.

An equilateral triangle is inscribed in the parabola y2 = Bx, with one of its vertices is the vertex of the parabola. Then, length of the side of that triangle is

  • 243 units

  • 163 units

  • 83 units

  • 43 units


388.

The point (3, 4) is the focus and 2x - 3y + 5 = 0 is the directrix of a parabola. Its latus rectum is

  • 213

  • 413

  • 113

  • 313


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389.

The radius of the circle passing through the foci of the ellipse x216 + y29 = 1 and having its centre at (0, 3) is

  • 6

  • 4

  • 3

  • 2


390.

The equation of the circle passing through (2, 0) and (0, 4) and having the minimum radius, is

  • x2 + y2 = 20

  • x2 + y2 - 2x - 4y = 0

  • x2 + y2 = 4

  • x2 + y2 = 16


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