[" Prove that the eurve "x^(2)+y^(2)+x+2y=0" and "x+2x-y],[" interscet orthogonally at the origin."]

Prove that the curve x^(2)+y^(2)+x+2y=0 and xy+2x-y=0 intersect orthogonally at the origin.

Prove that the curves 2y^(2)=x^(3) and y^(2)=32x cut each other orthogonally at the origin

Prove that the curves x^(2)+y^(2)=ax and x^(2)+y^(2)=by are cuts orthogonally.

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

If the circles x^(2)+y^(2)-2 x-2 y-7=0 and x^(2)+y^(2)+4 x+2 y+k=0 cut orthogonally, then the length of the common chord of the circles is

The two circles x ^(2)+y^(2)-2x +22y +5=0 and x ^(2) + y^(2) +14 x+6y +k=0 intersect orthogonally provided k is equal to-

If the two circles 2x^(2) +2y^(2) -3x+6y+k=0 and x^(2) +y^(2) -4x +10y +16=0 cut orthogonally, then the vlaue of k is-

Find k if the cirlces x^(2)+y^(2)-5x-14y-34=0 and x^(2)+y^(2)+2x+4y+k=0 are orthogonal to each other.