If the normal at one end of the latusrectum of an ellipse x2

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 Multiple Choice QuestionsMultiple Choice Questions

151.

If 5x - 12y + 10 = 0 and 12y - 5x + 16 = 0 are two tangents to a circle, then the radius of the circle is

  • 1

  • 2

  • 4

  • 6


152.

The area of the smaller segment cut off from the circle x2 + y2 = 9 by x = 1 is

  • 129sec-13 - 8

  • 9sec-13 - 8 sq unit

  • 8 - 9sec-13 

  • None of the above


153.

An equilateral triangle is inscribed in the parabola y2 = 4ax, whose vertex is at the vertex of the parabola. The length of its side is

  • 2a3

  • 4a3

  • 6a3

  • 8a3


154.

The period of the function f(x) = sinsinx5 is

  • 2π

  • 2π5

  • 10π

  • 5π


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155.

The foci of a hyperbola are (- 5, 18) and (10, 20) and it touches the Y-axis. The length of its transverse axis is

  • 100

  • 892

  • 89

  • 50


156.

The locus of mid-point of the line segment joining the locus to a moving point on the parabola y2 = 4ax is another parabola with directrix

  • x = - a

  • x = a

  • x = 0

  • x = a/2


157.

The equation of the ellipse with its centre at (1, 2), one locus at (6, 2) and passing through (4, 6) is

  • x - 1245 + y - 2220 = 1

  • x - 1220 + y - 2245 = 1

  • x + 1245 + y + 2220 = 1

  • None of the above


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158.

If the normal at one end of the latusrectum of an ellipse x2a2 + y2b2 = 1 passes through the one end of the minor axis, then

  • e4 - e2 + 1 = 0

  • e2 - e + 1 = 0

  • e2 + e + 1 = 0

  • e4 + e2 - 1 = 0


D.

e4 + e2 - 1 = 0

The coordinates of the extremity of the latusrectum which lies in the first quadrant are (ae, b2/a).

The equation of the normal at (x1, y1) is

a2xx1 - b2yy' = a2 - b2

Therefore, the equation of the normal at (ae, b2/a) is

a2xae - b2yy' = a2 - b2

 ax - aey = ea2 - b2 ax - aey = ea2e2     x - ey = ae2

This passes through the extremity of the minor axis i.e., (0, - b)

 0 + eb - ae3 = 0                    b = ae2                   b2 = a2e4      a21 - e2 = a2e4  e4 + e2 - 1 = 0


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159.

The equation of the curve in which the portion of the tangent included between the coordinate axes is bisected at the point of contact, is

  • a parabola

  • an ellipse

  • a circle

  • a hyperbola


160.

The solution of cos(x + y)dy = dx, is

  • y = tanx + y2 + C

  • y = cos-1yx

  • y = secyx + C

  • None of the above


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