The angle between the asymptotes of the hyperbola x2 - 3y2 = 3 is

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351.

The angle between the asymptotes of the hyperbola x2 - 3y2 = 3 is

  • π6

  • π4

  • π3

  • π2


C.

π3

Given equation of hyperbola is x2 - 3y2 = 1 x23 - y21 = 1Here, a2 = 3 and b2 = 1, a > bNow, equation of asymptote of this hyperbola is,y = ± bax y = ± 13x y = x3      . . . iand y = - x3   . . . iiLet slope of asymptote i is m1, = 13and slope of asymptote ii is m2 = - 13Let θ be the angle between both asymptote, thentanθ = m1 - m21 + m1m2 = 13 + 131 - 13 tanθ =  2323 = 3 tanθ = tan60°          θ = π3


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352.

If the area of the triangle formed by the pair of lines 8x- 6xy + y= 0 and the line 2x + 3y = a is 7, then a is equal to

  • 14

  • 142

  • 282

  • 28


353.

If the line x + 3y = 0 is the tangent at (0, 0) to the circle of radius 1, then the centre of one such circle is

  • (3, 0)

  • - 110, 310

  • 310, - 310

  • 110, 310


354.

A circle passes through the point (3, 4) and cuts the circle x+ y= aorthogonally; the locus of its centre is a straight line. If the distance of this straight line from the origin is 25, then a is equal to

  • 250

  • 225

  • 100

  • 25


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355.

The equation to the line joining the centres of the circles belonging to the coaxial system of circles 4x+ 4y- 12x + 6y - 3 + λ(x + 2y - 6) = 0 is

  • 8x - 4y - 15 = 0

  • 8x - 4y + 15 = 0

  • 3x - 4y - 5 = 0

  • 3x - 4y + 5 = 0


356.

Let x + y = k be a normal to the parabola y2 = 12x. If p is length of the perpendicular from the focus of the parabola onto this normal, then 4k - 2p2 is equal to

  • 1

  • 0

  • - 1

  • 2


357.

If the line 2x + 5y = 12 intersects the ellipse 4x+ 5y2 = 20 in two distinct points A and B,then mid-point of AB is

  • (0, 1)

  • (1, 2)

  • (1, 0)

  • (2, 1)


358.

Equation of one of the tangents passing through(2, 8) to the hyperbola 5x2 - y2 = 5 is

  • 3x + y - 14 = 0

  • 3x - y + 2 = 0

  • x + y + 3 = 0

  • x - y + 6 = 0


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359.

The area (in sq units) of the equilateral triangle formed by the tangent at (3, 0) to the hyperbola x2 - 3y2 = 3 with the pair of asymptotes of the hyperbola is

  • 2

  • 3

  • 13

  • 23


360.

The radius of the circle r = 12cosθ + 5sinθ IS

  • 512

  • 172

  • 152

  • None of these


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