If one of the lines in the pair of straight line given by 4x2&nbs

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 Multiple Choice QuestionsMultiple Choice Questions

161.

A pair of perpendicular lines passes through the origin and also through the points of intersection of the curve x2 + y2 = 4 with x + y = a, where a > 0. Then a is equal to

  • 2

  • 3

  • 4

  • 5


162.

If 3x2 - 11xy + 10y2 - 7x + 13y + k = 0 denotes a pair of straight lines, then the point of intersection of the lines is

  • (1, 3)

  • (3, 1)

  • (- 3, 1)

  • (1, - 3)


163.

The number of points P(x, y) with natural numbers as coordinates that lie inside the quadrilateral formed by the lines 2x + y = 2, x = 0, y = 0 and x + y = 5 is

  • 12

  • 10

  • 6

  • 4


164.

The image of the point (3, 8) in the line x + 3y = 7 is

  • (1, 4)

  • (4, 1)

  • (- 1, - 4)

  • (- 4, - 1)


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165.

The line joining the points A(2, 0) and B(3, 1) is rotated through an angle of 45°, about A in the anti-clockwise direction. The coordinates of B in the new position

  • 2, 2

  • 2, 2

  • (2, 2)

  • 2, 2


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166.

If one of the lines in the pair of straight line given by 4x2 + 6xy + ky2 = 0 bisects the angle between the coordinate axes, then k ∈

  • {- 2, - 10}

  • {- 2, 10}

  • {- 10, 2}

  • {2, 10}


C.

{- 10, 2}

Since, one of the lines represented by ax2 + 2hxy + ky2 = 0 bisect the angle between the axes therefore its equation is y = x.Since, y = x satisfies ax2 + 2hxy + by2 = 0, therefore

ax2 + 2hx2 +bx2 = 0            a + b2 = 4h2      . . . iNow for equation 4x2 + 6xy + ky2 = 0Here, a = 4, h = 3, b = kNow from eq. (i) 4 + k2 = 432 =36 4 + k = ± 6 k = 2, - 10Hence, k  - 10, 2


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167.

If ax2 + 2hxy +by2 + 2gx + 2fy + c = 0represents a pair of parallel lines, theng2 - acf2 - bc, is equal to

  • ab

  • ab

  • ba

  • ba


168.

If s and p are respectively the sum and the product of the slopes of the lines 3x- 2xy - 15y2 = 0, then s: p is equal to

  • 4 : 3

  • 2 : 3

  • 3 : 5

  • 3 : 4


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169.

If the lines 3x + 4y - 14 = 0 and 6x + By + 7 = 0 are both tangents to a circle, then its radius is

  • 7

  • 72

  • 74

  • 76


170.

If the circle x2 + y2 + 8x - 4y + c = 0 touches the circle x2 + y2 + 2x + 4y - 11 = 0 externally and cuts the circle x+y2 - 6x + By + k = 0 orthogonally, then k is equal to

  • 59

  • - 59 

  • 19

  • - 19 


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