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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
x = 2at2, y = at4
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Answer

The given equations are x = 2at2 and y = at4
Then, $\frac{\text{dx}}{\text{dt}}=\frac{\text{d}}{\text{dt}}(2\text{at}^2)=2\text{a}.\frac{\text{d}}{\text{dt}}(\text{t}^2)=4\text{at}\text{ and y}=\text{at}^4$
$\frac{\text{dx}}{\text{dt}}=\frac{\text{d}}{\text{dt}}(\text{at}^4)=\text{a}\frac{\text{d}}{\text{dt}}\text{(t}^4)=\text{a}.4.\text{t}^3=4\text{at}^3$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{\Big(\frac{\text{dy}}{\text{dt}}\Big)}{\Big(\frac{\text{dx}}{\text{dt}}\Big)}=\frac{4\text{at}^3}{4\text{at}}=\text{t}^2$

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