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Show that the line x/a + y/b = 1, touches the curve y = b . e-x/a at the point where the curve intersects the axis of y.
Show that the line x/a + y/b = 1, touches the curve y = b . e-x/a at the point where the curve intersects the axis of y.
Application of Derivatives | Class 12 | Exercise 1 | Maths | NCERT Exemplar
Show that the line x/a + y/b = 1, touches the curve y = b . e-x/a at the point where the curve intersects the axis of y.

Given curve condition, \[y\text{ }=\text{ }b\text{ }.\text{ }e-x/an\] and line condition \[x/a\text{ }+\text{ }y/b\text{ }=\text{ }1\]

Presently, let the directions of where the curve meets the y-axis be (0, y1)

Presently separating \[y\text{ }=\text{ }b\text{ }.\text{ }e-x/a\] the two sides w.r.t. x, we get

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 26

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 27

In this way, the condition of the curve crosses at \[\left( 0,\text{ }b \right)\] which is on the y-axis.

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