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Question

Without changing the direction of coordinate axes, origin is transferred to (h, k), so that the linear (one degree)

terms in the equation x2+y2−4x+6y−7=0 are eliminated. Then the point (h, k) is


A

(3, 2)

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B

(- 3, 2)

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C

(2, - 3)

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D

None of these

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Solution

The correct option is C

(2, - 3)


Putting x = x' + h, y = y' + k, the given equation transforms to

x2+y2+x(2h4)+y(2k+6)+h2+k27=0

To eliminate linear terms, we should have

2h - 4 = 0, 2k + 6 = 0 h = 2, k = -3

i.e., (h, k) = (2, -3).


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