The radius of the circle passing through the foci of the ellipse&

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 Multiple Choice QuestionsShort Answer Type

141.

Prove that for all values of m, except zero the straight line

y =  mx + am touches the parabola y2 = 4ax.


 Multiple Choice QuestionsMultiple Choice Questions

142.

If the lines 3x - 4y - 7 = 0 and 2x - 3y - 5 = 0 are two diameters of a circle of area 49π sq unit, then equation of the circle is

  • x2 + y2 + 2x - 2y - 62 = 0

  • x2 + y2 - 2x + 2y - 62 = 0

  • x2 + y2 - 2x + 2y - 47 = 0

  • x2 + y2 + 2x - 2y - 47 = 0


143.

The locus of middle point of chords of hyperbola 3x2 - 2y2 + 4x - 6y = 0 parallel to y = 2x is

  • 3x - 4y = 4

  • 3x - 4x + 4 = 0

  • 4x - 3y = 3

  • 3x - 4y = 2


144.

The equation of the common tangent touching the circle (x - 3)2 + y2 = 9 and parabola y = 4x above the x-axis is

  • √3y = 3x + 1

  • √3y = -( x + 3 )

  • √3y = x + 3

  • √3y = -( 3x + 1 )


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145.

The equation of the tangents to the ellipse 4x2 + 3y2 = 5 which are parallel to the line y = 3x + 7 are

  • y = 3x ± 1553

  • y = 3x ± 15512

  • y = 3x ± 9512

  • None of these


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146.

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

  • 4

  • 3

  • 12

  • 7/2


A.

4

Given equation of ellipse is x216 + y29 = 1

    a2 = 16, b2 = 9Then, e = 1 - b2a2 = 1 - 916 = 74

The coordinates of the foci are (± ae, 0) i.e., (± 7, 0)

So, radius of the circle = Distance between (± 7, 0) and (0, 3)

= 7 - 02 + 0 - 32= 7 + 9 = 4


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147.

The equation of the circle on the common chord of the circles (x - a)2 + y2 = a2 and x2 + (y + b)2 = b2 as diameter is

  • x2 + y2 = 2ab(bx + ay)

  • x2 + y2 = bx + ay

  • (a2 + b2)(x2 + y2) = 2ab(bx - ay)

  • (a2 + b2)(x2 + y2) = 2(bx + ay)


148.

The eccentricity of the hyperbola which passes through (3, 0) and (32, 2) is

  • 13

  • 133

  • 134

  • None of these


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149.

The line x - 1 = 0 is the directrix of the parabola y2 - kx + 8 = 0. Then, one of the value of k is

  • 18

  • 8

  • 4

  • 14


150.

The curve represented by

x = 3cost + sint, y = 4cost - sint is

  • ellipse

  • parabola

  • hyperbola

  • circle


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