Find the Plane

Geometry Level pending

The plane which is tangent to the sphere x 2 + y 2 + z 2 = 50 x^2+y^2+z^2=50 at the point ( 3 , 4 , 5 ) (3,4,5) has the form a x + b y + c z + d = 0 ax+by+cz+d=0 , find the value of a + b + c + d a+b+c+d


The answer is -38.

Hjalmar Orellana Soto by Hjalmar Orellana Soto , 24, Chile

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1 solution

T a n g e n t t o a c u r v e o f 2 n d d e g r e e x 2 + y 2 + z 2 = d a t p o i n t ( a , b , c ) i s g i v e n B y a x + b y + c z = d Tangent\quad to\quad a\quad curve\quad of\quad 2nd\quad degree\quad { x }^{ 2 }{ +y }^{ 2 }+{ z }^{ 2 }=d\quad at\quad point\quad \left( a,b,c \right) \\ is\quad given\quad By\quad ax+by+cz=d

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