y e − β x 2 = e α passes through ( 1 , 1 ) with tangent slope -2 . Let S 1 : x 2 + y 2 − 2 αx − 2 β y + α 2 + β 2 − 3 = 0 , and S 2 : x 2 + y 2 − 12 x − 22 y + 130 = 0 . Find 6 [ ( α /2 ) 2 + ( β

Question

y e − β x 2 = e α passes through ( 1 , 1 ) with tangent slope -2 . Let S 1 ​ : x 2 + y 2 − 2 αx − 2 β y + α 2 + β 2 − 3 = 0 , and S 2 ​ : x 2 + y 2 − 12 x − 22 y + 130 = 0 . Find 6 [ ( α /2 ) 2 + ( β /2 ) 2 ] .

TestHub · Accepted Answer

y = e α + β x 2 gives α + β = 0 at (1, 1); differentiation gives 2 β = − 2 . Thus ( α , β ) = ( 1 , − 1 ) and the result is 3.

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