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

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

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.

Find the differential equation for the equation x^(2)+y^(2)-2ax=0 .

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

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

Form differential equation for y=x+2ax^(2)

The tangent at the point P on the rectangular hyperbola xy=k^(2) with C intersects the coordinate axes at Q and R. Locus of the coordinate axes at triangle CQR is x^(2)+y^(2)=2k^(2)(b)x^(2)+y^(2)=k^(2)xy=k^(2)(d) None of these

Without rotating the original coordinate axes, to which point should origin be transferred,so that the equation x^(2)+y^(2)-4x+6y-7=0 is changed to an equation which contains no term of first degree?