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If $x-2=t^2, y=2 t$ are the parametric equations of the parabola $y^2=a(x-b)$, then the value of $a+b$ equals
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The correct answer is:
6
$\therefore x-2=t^2, y=2 t$ are the parametric equations of the parabola $y^2=a(x-b)$.
$\therefore$ It will satisfy the equation
$$
\begin{aligned}
x & =t^2+2, y=2 t \\
\Rightarrow \quad(2 t)^2 & =a\left(t^2+2-b\right) \Rightarrow 4 t^2=a t^2+a(2-b)
\end{aligned}
$$
Comparing coefficient of $t^2$ and constant term
$$
\begin{aligned}
a & =4 \text { and } 0=a(2-b) \\
b & =2 \\
\therefore \quad a+b & =4+2=6
\end{aligned}
$$
$\therefore$ It will satisfy the equation
$$
\begin{aligned}
x & =t^2+2, y=2 t \\
\Rightarrow \quad(2 t)^2 & =a\left(t^2+2-b\right) \Rightarrow 4 t^2=a t^2+a(2-b)
\end{aligned}
$$
Comparing coefficient of $t^2$ and constant term
$$
\begin{aligned}
a & =4 \text { and } 0=a(2-b) \\
b & =2 \\
\therefore \quad a+b & =4+2=6
\end{aligned}
$$
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