Sketch the region enclosed by the given curves. x = 7y², x = 4 + 6y²

Solution:

Given, the curves are

x = 7y² --- (1)

x = 4 + 6y² --- (2)

We have to sketch the region enclosed by the given curves.

x = 7y²

x = 4 + 6y²

By comparing (1) and (2),

7y² = 4 + 6y²

7y² - 6y² = 4

y² = 4

Taking square root,

y = ± 2

When y = 2, x= 7(2)² = 7(4) = 28

When y = -2, x = 7(-2)² = 7(4) = 28

So, the points are (28, 2) and (28, -2)

Therefore, the region enclosed by the given curves is shown in the graph.

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Sketch the region enclosed by the given curves. x = 7y², x = 4 + 6y²

Summary:

The region enclosed by the given curves. x = 7y², x = 4 + 6y² is shown in the above graph.