Question

# $$f(x, y) = x^2 + y^2 + 2ax + 2by + c = 0$$ represents a circle. If $$f(x, 0) = 0$$ has equal roots, each being $$2$$ and $$f(0, y) = 0$$ has $$2$$ and $$3$$ as it's roots, then centre of circle is

A
(2,52)
B
Data are not sufficient
C
(2,52)
D
Data are inconsistent

Solution

## The correct option is D Data are inconsistent$$x^2 +2ax + c = (x-2)^2$$$$\Rightarrow$$                 $$-2a = 4, c = 4$$$$\Rightarrow$$                 $$a = -2, c = 4$$                 $$y^2 + 2by + c = (y-2)(y-3)$$$$\Rightarrow$$                 $$-2b = 5, c = 6$$$$\Rightarrow$$      $$b = -\dfrac{5}{2}, c = 6$$ clearly the data are not consistent.Mathematics

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