marutkpadhy
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Find the radius of the circular section of the sphere of the sphere x^2 + y^2 + z^2 = 49 by the plane 2x+3y-z-5 \sqrt{14}= 0
Calculating Radius of Circular Section from Sphere and Plane Intersection
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MarkFL
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Suppose you solve the equation of the plane for $z$, and then substitute for $z$ into the equation of the sphere...what do you get?
Evgeny.Makarov
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View attachment 2708
I think it is easier to find the distance $d$ from the center of the sphere to the plane (recall the the distance from $(x_0,y_0,z_0)$ to $Ax+By+Cz+D=0$ is $\dfrac{Ax_0+By_y+Cz_0+D}{\sqrt{A^2+B^2+C^2}}$) and then find the radius $r$ of the required circular section from the right triangle.
I think it is easier to find the distance $d$ from the center of the sphere to the plane (recall the the distance from $(x_0,y_0,z_0)$ to $Ax+By+Cz+D=0$ is $\dfrac{Ax_0+By_y+Cz_0+D}{\sqrt{A^2+B^2+C^2}}$) and then find the radius $r$ of the required circular section from the right triangle.
