Answers edited by Raj

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