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Maths-

General

Easy

Question

The points on the curve $12 y equals x to the power of 3 end exponent$ whose ordinate and abscissa change at the same rate, are

$(- 2, - \frac{2}{3}), (2, \frac{2}{3})$
$(- \frac{2}{3}, - 2), (\frac{2}{3}, 2)$
$(- 2, - 2 / 3)$ only
$(2 / 3, 2)$ only

The correct answer is: $open parentheses negative 2 comma blank minus fraction numerator 2 over denominator 3 end fraction close parentheses comma open parentheses 2 comma fraction numerator 2 over denominator 3 end fraction close parentheses$

We have,
$12 y equals x to the power of 3 end exponent$

$rightwards double arrow 12 fraction numerator d y over denominator d t end fraction equals 3 x to the power of 2 end exponent fraction numerator d x over denominator d t end fraction$

$rightwards double arrow 12 equals 3 x to the power of 2 end exponent open square brackets because fraction numerator d y over denominator d t end fraction equals fraction numerator d x over denominator d t end fraction close square brackets$

$rightwards double arrow x equals plus-or-minus 2$

$therefore 12 y equals x to the power of 3 end exponent rightwards double arrow y equals plus-or-minus fraction numerator 2 over denominator 3 end fraction$

Hence, the points are $open parentheses 2 comma blank 2 divided by 3 close parentheses$ and $open parentheses negative 2 comma blank minus 2 divided by 3 close parentheses$

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