Page 6 - Jose Garcia_2013150017_grade12 ebook

5
2
2
2. Circle + − 2 + 4 − 20 = 0 translated by = ( ), so determine the
2
equation !

Solution :

if a point ( , ) is translated by ( , ) then its image is …..

′ +
( ) = ( ) + ( ) need to remind that ( ) + ( ) = ( )
′ +

we will look for the results of the shadow first,

′ 5 … +. . .
( ) = ( ) + ( ) = ( )
′ 2 … +. . .
′
′
The point image obtained is = + 5 dan = + 2, then we return to the
original point,
′
′
= + 5 ↔ x = … − . ..
′
′
= + 2 ↔ = … − . ..
then substitute x and y into the equation of the line.
2
′
( − 5) + ( − 2) − 2( − 5) + 4( − 2) − 20 = 0
2
′
′
′
2
′
′
′
= ( ) − 10 + 25 + ( ) − 4 + 4 − 2 − 10 + 4 − 8 − 20 = 0
′ 2
′ 2
′
2
′ 2
= ( ) − . . . + (… ) + . . . = 0
′

then the equation of the circle is
′ 2
( ) − 12 + ( ) + 11 = 0
′ 2
′

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