Change to polar coordinate the equations
`x^(2) + y^(2) = a^(2)`.

Change to polar coordinates the equations x^(2)-y^(2)=2ay

When origin is shifted to the point (4, 5) without changing the direction of the coordinate axes, the equation x^(2)+y^(2)-8x-10y+5=0 is tranformed to the equation x^(2)+y^(2)=K^(2) . Value of |K| is

Change the independent variable to o in the equation (d^(2)y)/(dx^(2))+(2x)/(1+x^(2))(dy)/(dx)+(y)/((1+x^(2))^(2))=0, by means of the transformation x=tan theta

Find the Cartesian coordinates (drawing a figure in each cas the points whose polar coordinates are: (5,(pi)/(4)) Change to polar coordinates the equations:

Transform the equation x^(2)+y^(2)=ax into polar form.

Keeping coordinate axes parallel, the origin is shifted to a point (1, –2), then transformed equation of x^2 + y^2 = 2 is -

Convert polar coordinate into Cartesian coordinate (2, pi/4)

By rotating the coordinates axes through 30^(@) in anticlockwise sense the eqution x^(2)+2sqrt(3)xy-y^(2)=2a^(2) change to

x coordinates of two points B and C are the roots of equation x^2 +4x+3=0 and their y coordinates are the roots of equation x^2 -x-6=0 . If x coordinate of B is less than the x coordinate of C and y coordinate of B is greater than the y coordinate of C and coordinates of a third point A be (3, -5) , find the length of the bisector of the interior angle at A.

Without changing the direction of the axes, the origin is transferred to the point (2,3). Then the equation x^(2)+y^(2)-4x-6y+9=0 changes to