P(5,5) is a point inside a circle x2 +y2-4x-6y-12=0. If the origin is translated to a certain point and the transformed equation is x2+y2=25, then the new point P=
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Answer:
The new point P is (3, 2).
Step-by-step explanation:
Let, the translation is x = X + h and y = Y + k.
The equation of the circle before translation is given by .
After translation the given equation will change to .
As per the given condition, the equation becomes .
Hence, 2h - 4 = 0, or, h = 2 and 2k - 6 = 0, or, k = 3.
The origin is translated to (2, 3).
As per our assumption, 5 = X + 2 or, X = 3 and 5 = Y + 3 or, Y = 2.
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