Question

the points on the curve y=x² at which y coordinate is changing six times as fast as x-coordinate is/are

a (2,4)
b (3,9)
c (3,9),(9,3)
d(6,2)​

Answer 1

Answer:

(6, 2)

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The points on the curve y = x² at which y coordinate is changing six times as fast as x-coordinate is/are

a. (2,4)

b. (3,9)

c. (3,9) , (9,3)

d. (6,2)

EVALUATION

Here the given equation of the curve is

$\sf y = {x}^{2} \: \: \: \: - - - (1)$

Differentiating both sides with respect to t we get

$\displaystyle \sf{ \frac{dy}{dt} = 2x\frac{dx}{dt} } \: \: \: \: - - - - (2)$

Now it is given that y coordinate is changing six times as fast as x-coordinate

Thus we get

$\displaystyle \sf{ \frac{dy}{dt} = 6\frac{dx}{dt} }$

Using Equation 2 we get

$\displaystyle \sf{ \implies 2x\frac{dx}{dt} = 6 \frac{dx}{dt} }$

$\displaystyle \sf{ \implies 2x= 6 }$

$\displaystyle \sf{ \implies x= 3 }$

From Equation 1 we get

$\sf y = {3}^{2}$

$\sf \implies \: y = 9$

Hence the required point = (3,9)

FINAL ANSWER

Hence the correct option is b. (3,9)

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