The focus of the conic $x^{2} - 6 x + 4 y + 1 = 0$ is

(2, 3)

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(3, 2)

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(3, 1)

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(1, 4)

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Solution

The correct option is B $(3, 2)$
The above equation can be represented as
$(x - 3)^{2} = - 4 (y - 2)$
Comparing it with the standard form of parabola $(x - h)^{2} = 4 a (y - k)$ , its focus is $(3, 2 - 1)$ i.e., $(3, 2)$

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\sqrt{2}

The equation of the conic with focus at (1, –1), directrix along x – y + 1 = 0 and with eccentricity $\sqrt{2}$ is

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