Find the position of the point
$(- 2, 2)$ with respect to the parabola $y^{2} - 4 y + 9 x + 13 = 0$

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Solution

$\begin{matrix} (- 2, 2) a r e p o i n t s a n d p a r a b o l a \Rightarrow y^{2} - 4 y + a x + 3 = 0 \Rightarrow y^{2} - 4 y + 4 + 9 x + 9 = 0 k {(y - 2)}^{2} = - 9 (x + 1) \Rightarrow y^{2} = - 9 x \to (i) t h e n, s a t i s f y p o i n t s (- 2, 2) i n e q . (i) \Rightarrow {(y - 2)}^{2} + 9 (x + 1) = 0 \Rightarrow {(2 - 2)}^{2} + 9 (- 2 + 1) = 0 \Rightarrow 0 - 9 < 0 (n e g a t i v e) S o, i t i s l i e s i n s i d e t h e p a r a b o l a \end{matrix}$

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