The equation of a tangent line to the parabol | vedclass

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(A) The equation of a tangent to the parabola $y^2 = 4ax$ with slope $m$ is $y = mx + \frac{a}{m}$.Here,$4a = 8$,so $a = 2$.The equation of the tangen

Vedclass · Accepted Answer

$y = 2x + 1$

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(A) The equation of a tangent to the parabola $y^2 = 4ax$ with slope $m$ is $y = mx + \frac{a}{m}$.Here,$4a = 8$,so $a = 2$.The equation of the tangent is $y = mx + \frac{2}{m}$.Since it passes through the point $(1, 3)$,we substitute $x = 1$ and $y = 3$:$3 = m(1) + \frac{2}{m}$$3 = m + \frac{2}{m}$$m^2 - 3m + 2 = 0$$(m - 1)(m - 2) = 0$Thus,$m = 1$ or $m = 2$.For $m = 1$,the tangent is $y = 1x + \frac{2}{1} \Rightarrow y = x + 2$.For $m = 2$,the tangent is $y = 2x + \frac{2}{2} \Rightarrow y = 2x + 1$.Comparing with the given options,$y = 2x + 1$ is present.

The equation of a tangent line to the parabola $y^2 = 8x$,which passes through the point $(1, 3)$,is:

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