I am confuse because definition related to these two is different however the equation to find these two planes (i.e. plane of contact and polar plane) is same. Let say equation of sphere is $$x^2+y^2+z^2+2ux+2vy+2wz+d=0$$ where $x,y,z$are variables and others are constant. And an exterior point is $A(x_1,y_1,z_1)$. Then equation of plane of contact of sphere wrt to point $A$ and equation of polar plane of sphere wrt $A$ as a pole is same as equation of tangent i.e. $$xx_1+yy_1+zz_1+u(x+x_1)+v(y+y_1)+w(z+z_1)+d=0$$ So, what’s the difference?
2026-03-29 12:47:24.1774788444
What is the difference between Plane of contact of a sphere and polar plane of sphere?
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