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Engineering
124 Views   |  

If A(-2,1), B(2,3) and C(-2,-4) are three points, then the angle between BA and BC is

  • Option 1)

    \tan ^{-1}\left ( \frac{3}{2} \right )

  • Option 2)

    \tan ^{-1}\left ( \frac{2}{3} \right )

  • Option 3)

    \tan ^{-1}\left ( \frac{7}{4} \right )

  • Option 4)

    None

 
  Angle between two lines (?) - - wherein Here are the slope of two lines     So, acute angle  Option 1) This solution is incorrect Option 2) This solution is correct Option 3) This solution is incorrect Option 4) None This solution is incorrect
Engineering
103 Views   |  

If (4,-2) is a point on the circle x^{2}+y^{2}+2gx+2fy+c=0

which is concentric to  x^{2}+y^{2}-2x+4y+20=0\:then\:value\:of C\: is

  • Option 1)

    -4

  • Option 2)

    0

  • Option 3)

    4

  • Option 4)

    1

 

Since both circles are concentric so coordinate of their centre is (1,-2)=(-g ,-f) 

Put the given value of (x,y)=(4,-2) and "g and f "

4^2+(-2)^2+2×(-1)×4+2×2×(-2)+C=0

=> C= -4

Thank you 

 

Engineering
103 Views   |  

Find the equation of the hyperbola whose directrix is 2x + y = 1, focus (1, 2) and eccentricity \sqrt{3} 

  • Option 1)

    7x2 - 2y2 + 12xy - 2x + 14y - 22 = 0

  • Option 2)

    7x2 - 2y2 + 2xy - 2x + 14y - 22 = 0

  • Option 3)

    7x2 - 2y2 + xy - 14x + 2y - 22 = 0

  • Option 4)

    none of the above

 
  Eccentricity - The ratio of a distance of point from focus to distance from fixed line. - wherein   It is donated by .    & Directrix - The fixed straight line of a conic section. - wherein    & Focus - The fixed point of a conic section - wherein     Option 1) 7x2 - 2y2 + 12xy - 2x + 14y - 22 = 0 This solution is correct Option 2) 7x2 - 2y2 + 2xy - 2x + 14y - 22 = 0 This solution is...
Engineering
107 Views   |  

Equation of the hyperbola with eccentricity 3/2 and foci at (\pm2, 0) is

  • Option 1)

    \frac{x^{2}}{4}-\frac{y^{2}}{9}=\frac{4}{9}

  • Option 2)

    \frac{x^{2}}{9}-\frac{y^{2}}{4}=\frac{4}{9}

  • Option 3)

    \frac{x^{2}}{4}-\frac{y^{2}}{9}=1

  • Option 4)

    None of these

 
  Coordinates of foci - - wherein For the Hyperbola                                          equation    Option 1) This solution is incorrect Option 2) This solution is incorrect Option 3) This solution is incorrect Option 4) None of these This solution is correct
Engineering
115 Views   |  

Equation of tangents to ellipse \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 , which are perpendicular to the line 3x + 4y= -7

  • Option 1)

    4x-3y=\pm 6\sqrt{5}

  • Option 2)

    4x-3y=\pm \sqrt{12}

  • Option 3)

    4x-3y=\pm \sqrt{2}

  • Option 4)

    4x-3y=\pm {1}

 
  Standard equation -   - wherein Semi major axis Semi minor axis     Slope of tangent  So, equation of tangent at  where,   &                                         equation  Option 1)   This solution is correct Option 2) This solution is incorrect Option 3) This solution is incorrect Option 4) This solution is incorrect
Engineering
329 Views   |  

A line passes through the point of intersection of the lines 100x+50y-1=0 and 75x+25y+3=0 and makes equal intercepts on the axis, its equation is  

  • Option 1)

    25x+25y-1=0

  • Option 2)

    5x-5y+3=0

  • Option 3)

    25x+25y-4=0

  • Option 4)

    25x-25y+6=0

 
  Family of straight lines -   - wherein   are the equations of the lines and is a constant.    family of lines: intercept  &  So, equal intercepts mean Option 1) 25x+25y-1=0 This solution is incorrect. Option 2) 5x-5y+3=0 This solution is incorrect. Option 3) 25x+25y-4=0 This solution is incorrect. Option 4) 25x-25y+6=0 This solution is incorrect.
Engineering
500 Views   |  

A double ordinate of the parabola y2 = 8 px is of length 16p. The angle subtended by it at the vertex of the parabola is

  • Option 1)

    \frac{\pi}{4}

  • Option 2)

    \frac{\pi}{2}

  • Option 3)

    \frac{\pi}{3}

  • Option 4)

    none of these

 
  Length of the latus rectum -   - wherein For the parabola.    & End point of latus rectum - - wherein For the parabola.     Also,  Now,  So,  angle subtended     when,  So,  Option 1) This solution is incorrect Option 2) This solution is correct Option 3) This solution is incorrect Option 4) none of these This solution is incorrect
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