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  • If x = a cos t, y = a sin t,  then <img alt="\frac{\mathrm{d}^2 \mathrm{y}}{\mat

If x = a cos t, y = a sin t,  then \frac{\mathrm{d}^2 \mathrm{y}}{\mathrm{dx}^2} \text { at } \mathrm{t}=\frac{\pi}{4} \text { is }

Option: 1

\frac{a}{2 \sqrt{2}}


Option: 2

-\frac{a}{2 \sqrt{2}}


Option: 3

\frac{2 \sqrt{2}}{a}


Option: 4

-\frac{2 \sqrt{2}}{a}


Answers (1)

best_answer

Clearly x2 + y2 = a2 and y(π/4) =\mathrm{a} / \sqrt{2}, \mathrm{x}(\pi / 4)=\mathrm{a} / \sqrt{2}

Differentiating we get,                                                      2x + 2yy1 = 0  ⇒  y1 = -\frac{x}{y} \text {, so } y_1(\pi / 4)=-1

Now x + yy1 = 01+y_1^2+y_2=0

y_2(\pi / 4)=-\frac{1+\left(y_1(\pi / 4)\right)^2}{y(\pi / 4)}=\frac{-2 \sqrt{2}}{a}

 

Posted by

Divya Prakash Singh

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