 Hi and welcome to our session. Let us discuss the following question. The question says, find the equation of a sphere passing through 3 0 0 0 minus 1 0 0 0 minus 2 and having center on the plate, 3x plus 2y plus 4z equals to 1. Let's now begin with the solution. Let the equation of required sphere be plus y squared 2y plus 2wz plus d equals to 0. Now add 0 minus 1 0 0 0 minus 2. Therefore it must satisfy this equation. Right? So let's first substitute 3 in place of x, 0 in place of y and 0 in place of z in this equation. So we have 3 squared plus 0 squared plus 0 squared plus 2u into 3 plus 2v into 0 plus 2w into 0 plus d equals to 0. This implies 90 is equal to 0 and this implies equal to minus 9 minus d divided by 6. Equation of sphere. So we get 0 squared plus minus 1 squared plus 0 squared plus 2u into 0 plus 2v into minus 1 plus 2w into 0 plus d equals to 0. This implies v is equal to 1 plus d divided by so we have 0 squared plus 0 squared plus minus 2 squared into 0 plus 2v into 0 w into minus 2 plus d equals to 0. This implies 4 4w plus d is equal to 0 and this implies w is equal to divided by d minus w having equation as u plus 2 into minus v plus 4 into minus w is minus 3u minus 2v minus 4w is equal to 1 plus 4w is equal to minus 5. Now we will substitute d divided by 2 divided by 4. This implies minus 9 minus d is equal to minus 2 minus 9 minus d plus d divided by d here so we get minus 9 minus 1 divided by 6. This is equal to now v is equal to divided by 2 is equal to minus 1 so we get v as d divided by 2 minus 1. So we have 4 minus 1 divided by 2 and this is equal to required equation of spirit completes the session bye.