If the straight line y = 4x + c is a tangent to the ellipse 

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 Multiple Choice QuestionsMultiple Choice Questions

231.

The equation of the tangent to the parabola y2 = 8x, which is parallel to the line 2x - y + 7 = 0, will be

  • y = x + 1

  • y = 2x + 1

  • y = 3x + 1

  • y = 4x + 1


232.

The distance of a point on ellipse x26 + y22 = 1 from its centre is 2. The eccentric angle of the point will be

  • π4 or π3

  • π3 or 3π5

  • π4 or 3π4

  • None of these


233.

The distance between the foci of a hyperbola is 16 and its eccentncity is 2. Its equation will be

  • x2 - y2 = 1

  • x2 - y2 = 20

  • x2 - y2 = 4

  • x2 - y2 = 32


234.

Equation of the circle which passes through the origin and cuts intercepts of lengths a and b on axes is

  • x2 + y2 + ax + by = 0

  • x2 + y2 + ax - by = 0

  • x2 + y2 + bx + ay = 0

  • None of the above


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235.

If focus ofa parabolais at (3, 3) and its directrix is 3x - 4y = 2, then its latusrectum is

  • 2

  • 3

  • 4

  • 5


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236.

If the straight line y = 4x + c is a tangent to the ellipse x28 + y24 = 1, then c will be equal to

  • ± 4

  • ± 6

  • ± 1

  • ± 132


D.

± 132

Given, equation of the ellipse is     x28 + y24 = 1We know that, condition of tangency to an ellipse is    c2 = a2m2 + b2    c2 = 128 + 4 = 132 c = ± 132


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237.

The distance between the foci of a hyperbola is 16 and its eccentricity is - 2. Its equation will be

  • x2 - y2 = 32

  • y2 - x2 = 32

  • x2 - y2 = 16

  • y2 - x2 = 16


238.

The number of common tangents that can be drawn to the circles x2 + y2 - 4x - 6y - 3 = 0 and x2 + y2 + 2x + 2y + 1 = 0 is

  • 1

  • 2

  • 3

  • 4


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239.

If two circles (x - 1)2 + (y - 3)2 = r2 and x2 + y2 - 8x + 2y + 8 = 0 intersect in two distinct points, then

  • 2 < r < 8

  • r < 2

  • r = 2

  • r > 2


240.

The equation of the tangent at the vertex of the parabola x2 + 4x + 2y = 0, is

  • x = - 2

  • x = 2

  • y = - 2

  • y = 2


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