The equation x2 - 7xy + 12y2 = 0 represents a from Mathematics C

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 Multiple Choice QuestionsMultiple Choice Questions

241.

The distance between the directrices of the ellipse x24 + y29 = 1 is

  • 95

  • 185

  • 245

  • None of these


242.

The equation of the normal to the hyperbola x2 - 16y2 - 2x - 64y - 72 = 0 at the point (- 4, - 3) is

  • 5x + 16y + 79 = 0

  • 16x + 5y + 97 = 0

  • 16x + 5y + 79 = 0

  • 5x + 16y + 97 = 0


243.

The centre of the circle which circumscribes the square formed by x2 - 8x + 12 = 0 and y2 - 14y + 45 = 0 is

  • (4, 5)

  • (3, 4)

  • (9, 5)

  • (4, 7)


244.

If e1 and e2 are the eccentricities of the hyperbolas x2a2 - y2b2 = 1 and x2a2 - y2b2 = - 1, then the value of 1e12 + 1e22 is

  • 3

  • 2

  • 1

  • 12


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245.

The point of contact of 3x + 4y + 7 = 0 and x2 + y2 - 4x - 6y -12 = 0 is

  • (1, 1)

  • (- 1, 1)

  • (1, - 1)

  • ( -1, - 1)


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246.

The equation x2 - 7xy + 12y2 = 0 represents a

  • circle

  • pair of parallel straight lines

  • pair of perpendicular straight lines

  • pair of non-perpendicular straight lines


D.

pair of non-perpendicular straight lines

 Given equation isx2 - 7xy + 12y2 = 0On comparing with ax2 + 2hxy + by2 = 0 a = 1, h = - 72, b = 12 m1 + m2 = - 2hband     m1m2 = ab m1 + m2 = 712and     m1m2 = 112        ...iNow, m1 - m2 = m1 + m22 - 4m1m2                            = 7122 - 4 × 112                            = 49 - 48144 = 1144 = 112        m1 - m2 = 112      ...(ii)On solving Eqs. (i) and (ii), we getm1 = 13 and m2 = 312Now, tanθ = m1 - m21 + m1m2                   = 13 - 3121 + 13 × 312    tanθ = 1121312 = 113  0Hence, given equation is a non-perpendicular straight lines.


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247.

The locus of z given by z - 1z +1 = 1 is

  • a parabola

  • an ellipse

  • a circle

  • a straight line


248.

A conic section represents a circle, if its eccentricity e is

  • e < 0

  • e > 0

  • e = 0

  • None of these


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249.

The equation of circle passing through the points (0, 2) (3, 3) and having its centre on the x-axis is

  • x2 + y2 - 14x - 12 = 0

  • 3x2 + 3y2 - 22x - 4 = 0

  • 3x2 + 3y2 - 14x - 12 = 0

  • None of the above


250.

The equation of a circle passing through origin and radius is a, is

  • (x - a)2 + (y - a)2 = a2

  • x2 + y2 = a2

  • (x - a)2 + y2 = a2

  • None of the above


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