The product of the perpendicular distances from any point on the

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 Multiple Choice QuestionsMultiple Choice Questions

341.

If the circle x2 + y2 + 2x + 3y + 1 = 0 cuts another circle x2 + y+ 4x + 3y + 2 = 0 in A and B, then the equation of the circle with AB as a diameter is

  • x2 + y2  + x + 3y + 1 = 0

  • 2x2 + 2y2  + 2x + 6y + 1 = 0

  • x2 + y2  + x + 6y + 1 = 0

  • 2x2 + 2y2  + x + 3y + 1 = 0


342.

The equation of the hyperbola which passes through the point (2, 3) and has the asymptotes 4x + 3y - 7 = 0 and x - 2y - 1 = 0 is

  • 4x2 + 5xy - 6y2 - 11x + 11y + 50 = 0

  • 4x2 + 5xy - 6y2 - 11x + 11y - 43 = 0

  • 4x2 - 5xy - 6y2 - 11x + 11y + 57 = 0

  • x2 - 5xy - y2 - 11x + 11y - 43 = 0


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343.

The product of the perpendicular distances from any point on the hyperbola x2a2 - y2b2 = 1 to its asymtotes is

  • a2b2a2 - b2

  • a2b2a2 + b2

  • a2 + b2a2b2

  • a2 - b2a2b2


B.

a2b2a2 + b2

Let asecθ, btanθ be any point  on  the hyperbolax2a2 - y2b2 = 1The equation of the asymptotes of the given hyperbola arexa + yb = 0 and xa - yb = 0Now, P1 = length of the perpendicular from(a secθ, b tanθ) onxa + yb = 0 P1 = secθ + tanθ1a2 + 1b2     ...iP2 = length of  the  perpendicular from (a secθ, b tanθ) onxa - yb = 0

     P2 = secθ - tanθ1a2 + 1b2     ...ii P1P2 = secθ + tanθ1a2 + 1b2secθ - tanθ1a2 + 1b2               = sec2θ - tan2θ1a2 + 1b2 = 1a2 + b2a2b2 P1P2 = a2b2a2 + b2


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344.

If the lines 2x + 3y +12 = 0, x - yy + k = 0 are conjugate with respect to the parabola y2 = 8x, then k is equal to

  • 10

  • 72

  • - 12

  • - 2


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345.

Find the equation to the parabola, whose axis parallel to they-axis and which passes through the points (0, 4), (1, 9) and (4, 5) is

  • y = - x+ x + 4

  • y = - x+ x + 1

  • y = - 1912x2 + 7912x + 4

  • y = - 1912x2 + 8912x + 4


346.

If the line y = 2x + c is a tangent to the circle x2 + y2 = 5, then a value of

  • 2

  • 3

  • 4

  • 5


347.

A line segment AM = a moves in the XOY plane such that AM is parallel to the X-axis. If A moves along the circle x2 + y= a2, then the locus of M is

  • x2 + y= 4a2

  • x2 + y= 2ax

  • x2 + y= 2ay

  • x2 + y= 2ax + 2ay


348.

If a chord of the parabola y = 4x passes through its focus and makes an angle 0 with the X-axis, then its length is

  • 4cos2θ

  • 4sin2θ

  • 4csc2θ

  • 4sec2θ


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349.

If the straight line y = mx + c is parallel to the axis of the parabola y = bx and intersects the parabola at c28, c, then the length of the latus rectum is

  • 2

  • 3

  • 4

  • 8


350.

The eccentricity of the ellipse x2 + 4y2 + 2x + 16y + 13 = 0 is

  • 32

  • 12

  • 13

  • 12


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