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If the parabola $y^{2}=4$ ax passes through the point $(1,-2)$, then the tangent at this point is
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Verified Answer
The correct answer is:
$x+y+1=0$
Since the parabola $y^{2}=4 a x$ passes through the point $(1,-2)$,
$$
\therefore(-2)^{2}=4 \mathrm{a}(1) \Rightarrow \mathrm{a}=1
$$
Equation of tangent to the parabola at $(1,-2)$ is
$\mathrm{yy}_{1}=2 \mathrm{a}\left(\mathrm{x}+\mathrm{x}_{1}\right)$ or
$$
y(-2)=2(1)(x+1) \text { or } x+y+1=0
$$
$$
\therefore(-2)^{2}=4 \mathrm{a}(1) \Rightarrow \mathrm{a}=1
$$
Equation of tangent to the parabola at $(1,-2)$ is
$\mathrm{yy}_{1}=2 \mathrm{a}\left(\mathrm{x}+\mathrm{x}_{1}\right)$ or
$$
y(-2)=2(1)(x+1) \text { or } x+y+1=0
$$
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