Question

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=

Answer 1

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 $x^{2} + y^{2} -4x-6y-12=0$.

After translation the given equation will change to $(X + h)^{2} + (Y + k)^{2} -4(X + h)-6(Y + k)-12=0\\\\X^{2} + 2Xh + h^{2} + Y^{2} + 2Yk + k^{2} -4X - 4h - 6Y - 6k - 12 = 0\\X^{2} + Y^{2} + (2h - 4)X + (2k - 6)Y + h^{2} + k^{2} - 4h - 6k - 12 = 0$.

As per the given condition, the equation becomes $X^{2} + Y^{2} = 25$.

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.