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Find the co-ordinates of the point on the curve √x + √y = 4 at which tangent is equally inclined to the axes.
Application of Derivatives | Class 12 | Exercise 1 | Maths | NCERT Exemplar
Find the co-ordinates of the point on the curve √x + √y = 4 at which tangent is equally inclined to the axes.

ACCORDING TO EQUATION OF CURVE,

    \[\surd x\text{ }+\text{ }\surd y\text{ }=\text{ }4\]

Presently, let (x1, y1) be he required point on the bend

SO ,

    \[\surd x1\text{ }+\text{ }\surd y1\text{ }=\text{ }4\]

separating both the sides w.r.t. x1, we get

squaring both the sides, we get

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 22

    \[y1/x1\text{ }=\text{ }1\Rightarrow y1\text{ }=\text{ }x1\]

PUT THE VALUE OF Y,

    \[\surd x1\text{ }+\text{ }\surd y1\text{ }=\text{ }4\]

    \[\surd x1\text{ }+\text{ }\surd x1\text{ }=\text{ }4\Rightarrow 2\surd x1\text{ }=\text{ }4\Rightarrow \surd x1\text{ }=\text{ }2\Rightarrow x1\text{ }=\text{ }4\]

    \[As\text{ }y1\text{ }=\text{ }x1\]

    \[\Rightarrow y1\text{ }=\text{ }4\]

NOW ,

point is

    \[\left( 4,\text{ }4 \right).\]

i

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