The length of tangent drawn at (4, 4) on the curve $y^2 = 4x$ is ?  Option 1) $3\sqrt5$ Option 2) $4\sqrt5$ Option 3) $5\sqrt5$ Option 4) $6\sqrt5$

H Himanshu

As we have learned

Length of Tangent -

$L_{T}=\frac{y}{y'}\sqrt{1+y'^{2}}$

- wherein

Where $Where\:\:y'=\frac{dy}{dx}$

length of tangent $= \frac{y}{y^{1}}\sqrt{1+(y^{1})^{2}}$

$\because y^{2}=4x\Rightarrow 2yy'=4 \Rightarrow y'= 2/y\Rightarrow y'$  at (4,4) is 1/2

$\therefore$ length = $\frac{4}{1/2}\sqrt{1+1/4}=4\sqrt5$

Option 1)

$3\sqrt5$

Option 2)

$4\sqrt5$

Option 3)

$5\sqrt5$

Option 4)

$6\sqrt5$

Exams
Articles
Questions