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Slope Point Form of a Line

The circle ...

Question

The circle $x^{2} + y^{2} + 4 x - 7 y + 12 = 0$ cuts an intercept on y-axis equal to-

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Solution

if it touches the y-axis then $x = 0$ should satisfy the Equation
$0 + y^{2} + 0 - 7 y + 12 = 0 \Rightarrow y^{2} - 4 y - 3 y + 12 = 0 \Rightarrow y (y - 4) - 3 (y - 4) = 0 \Rightarrow (y - 3) (y - 4) = 0 \Rightarrow y = 3, 4$

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Slope Point Form of a Line

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