Center on the y-axis and touching the line x+y+2=0 at (2, -4)

June Mejia

June Mejia

Answered question

2022-08-06

Center on the y-axis and touching the line x+y+2=0 at (2, -4)

Answer & Explanation

Kasey Bird

Kasey Bird

Beginner2022-08-07Added 13 answers

Centre at (0,k)
and radius =distance of x+y+2=0 from (0,k) = ( k + 2 ) 2
And also (2,-4) lies on circle
So r a d i u s 2 = 4 + ( k + 4 ) 2 = ( k + 2 ) 2 2 8 + 2 k 2 + 32 + 16 k = k 2 + 4 + 4 k k 2 + 12 k + 36 = 0 ( k + 6 ) 2 = 0
k=-6
So radius = 8 2 = 2 So eqn  = x 2 + ( y + 6 ) 2 = 32 x 2 + y 2 + 12 y + 4 = 0 ( a n s )

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