Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsMedium2 minPYQ_2019

MathematicsMediumsingle choice

The distance between the origin and the normal to curve $y = e^{2 x} + x^{2}$ at $x = 0$ is

Answer:

Solution:

We have,

$y = e^{2 x} + x^{2}$

at $x = 0, y = 1$

$\frac{d y}{d x} = 2 e^{2 x} + 2 x$

${(\frac{d y}{d x})}_{x = 0} = 2$

$∴$ Equation of normal at $(0, 1)$ is

$y - 1 = - \frac{1}{2} (x)$

$\Rightarrow x + 2 y - 2 = 0$

$∴$ Distance from $(0, 0)$ from normal $= \frac{2}{\sqrt{5}}$

Stream:BITSATSubject:MathematicsTopic:Application of DerivativeSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: PYQ_2019

Loading discussions...