The equation of the plane through the intersection of the planes

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 Multiple Choice QuestionsShort Answer Type

61.

Find the angle subtended by the double ordinate of length 2a of the parabola y2 = ax at its vertex.


62.

The equation to the pairs of opposite sides of a parallelogram are x- 5x + 6 = 0 and y2 - 6y + 5. Find the equations its diagonals.


 Multiple Choice QuestionsMultiple Choice Questions

63.

A common tangent to 9x2 - 16y2 = 144 and x2 + y2 = 9 is

  • y = 37x + 157

  • y = 327x + 157

  • y = 237x + 157

  • None of these


64.

The locus of a point P which moves such that 2PA = 3PB, where A(0, 0) and B(4,- 3) are points, is

  • 5x2 - 5y2 - 72x + 54y + 225 = 0

  • 5x2 + 5y2 - 72x + 54y + 225 = 0

  • 5x2 + 5y2 + 72x - 54y + 225 = 0

  • 5x2 + 5y2 - 72x - 54y - 225 = 0


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65.

The points P is equidistant from A(1, 3), B (- 3, 5) and C(5, - 1), then PA is equal to

  • 5

  • 55

  • 25

  • 510


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66.

The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y - z + 4 = 0 and parallel to X-axis, is

  • y - 3z + 6 = 0

  • 3y - z + 6 = 0

  • y + 3z + 6 = 0

  • 3y - 2z + 6 = 0


A.

y - 3z + 6 = 0

The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y - z + 4 = 0 is

(x + y + z - 1) + λ(2x + 3y - z + 4) = 0

or (2λ + 1)x + (3λ + 1)y + (1 - λ)z + 4λ - 1 = 0     ...(i)

It is parallel to x-axis i.e., x1 = y/0 = z/0

 λ = - 1/2

On substituting λ = - 1/2 in Eq. (i) we get y - 3z + 6 = 0 as the equation of the required plane.


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67.

If the direction cosines of two lines are connected by the equations l + m + n = 0, l2 + m2 - n2 = 0, then the angle between the lines is

  • π4

  • π6

  • π2

  • π3


68.

The equation of the plane which contains the origin and the line of intersection of the planes r · a = d1 and r · b = d2, is

  • r . (d1a + d2b) = 0

  • r . (d2a - d1b) = 0

  • r . (d2a + d1b) = 0

  • r . (d1a - d2b) = 0


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69.

If from a point P(a, b, c) perpendiculars PA and PB are drawn to YZ and ZX - planes, then the equation of the plane OAB is

  • bcx + cay + abz = 0

  • bcx + cay - abz = 0

  • - bcx + cay + abz = 0

  • bcx - cay + abz = 0


70.

If (2, 7, 3) is one end of a diameter of the sphere x2 + y+ z- 6x - 12y - 2z + 20 = 0, then the coordinates of the other end of the diameter are

  • (- 2, 5, - 1)

  • (4, 5, 1)

  • (2, - 5, 1)

  • (4, 5. - 1)


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