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If $(2, k)$ is a point on the parabola passing through the points $(1,-3),(-1,5),(0,2)$ and having its axis parallel to the $Y$-axis, then $k$ is equal to
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The correct answer is:
-10
Let equation of parabola is
Eq. (i) passes through $(1,-3),(-1,5)$ and $(0,2)$.
From Eqs. (ii), (iii) and (iv),
From Eq. (i), $\quad \begin{aligned} & a=-1, b=-4, c= \\ & y=-x^2-4 x+2\end{aligned}$
$\because(2, k)$ lies on the above parabola.
$$
\therefore \quad k=-4-8+2=-10
$$
Eq. (i) passes through $(1,-3),(-1,5)$ and $(0,2)$.
From Eqs. (ii), (iii) and (iv),
From Eq. (i), $\quad \begin{aligned} & a=-1, b=-4, c= \\ & y=-x^2-4 x+2\end{aligned}$
$\because(2, k)$ lies on the above parabola.
$$
\therefore \quad k=-4-8+2=-10
$$
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