Answers edited by Raj

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• Show that the plane #2x-4y-z+9=0# touches the sphere which passes through #(1,1,6)# and whose centre is #(2,-3,4)#. Also, find the point of contact.?
  
• How to find the area of the loop of the curve #x(x^2+y^2)=a(x^2-y^2)#?
  
• What is the angle between two lines whose direction ratios satisfy following equations?
  
• Differentiate #tan^-1 ((2x)/(1-x^2))# with respect to #sin^-1 ((2x)/(1+x^2))#?
  
• Find the maximum and minimum values for the function #f# defined by #f(x) = 2sinx + cos2x# in the interval #[0, pi/2]#?
  
• What surface represented by #x^2+y^2=9z#? Obtain the section of this surface by the plane #y=0# ?
  
• How to find solution set in #RR^3# of #x-pi=5#?
  
• Find the equation of the line which is parallel to the line #3x+4y=1# and passes through the midpoint of the line segment joining #(1,2)# and #(-2,1)#. Find the distance of this line from the given line.?
  
• What is the equations of the tangents of the conic #x^2+4xy+3y^2-5x-6y+3=0# which are parallel to the line #x+4y=0#?
  
• Find the coordinates of the vertices and foci, eccentricity? #x^2-8x+2y+7=0#
  
• Find the equation of the tangent and normal to the curve #x^2+y^2+4x+3y-25=0# at #(-3, 4)#?
  
• Find the domain of the function #f# defined by #f(x) = 1/sqrt(5x-x^2-6)#?
  
• Give a real life situation problem which is mathematically translated into #2x+y+2z=18#?