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

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:

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 polar coordinates of the points whose cartesian coordinates are (-2, -2)

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

If x,y and z are eliminated from the equations x=cy+bz, y=az+cx" and z=bx+ay, then a^(2)+b^(2)+c^(2)+2abc=

The equation of the parabola whose vertex is (a,0) and the directrix has the equation x+y=3a is x^(2)+y=3xy+6ax+10ay+7a^(2)=0x^(2)-2xy+y^(2)-6ax+10ay+7a^(2)=0x^(2)-2xy+y^(2)+6ax+10ay+7a^(2)=0 None of these

Examine the consistency of the system of equations x2x+3y+2z=2ax+ay+quad 2aquad z=4

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

The differential equation of all circle in the first quadrant touch the coordinate is (a) (x-y)^(2)(+y')^(2))=(x+yy')^(2) (b) (x-y)^(2)(+y')^(2))=(x+y')^(2) ( c ) (x-y)^(2)(+y')=(x+yy')^(2) (d) None of these

The line x+14y=25 is the polar of the ellipse x^(2)+4y^(2)=25. Find coordinates of the pole.