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Solution for Find the Coordinates of the Point on the Curve Y2 = 3 − 4x Where Tangent is Parallel to the Line 2x + Y− 2 = 0 ? - CBSE (Science) Class 12 - Mathematics

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Question

Find the coordinates of the point on the curve y2 = 3 − 4x where tangent is parallel to the line 2x + y− 2 = 0 ?

Solution

Let (x1, y1) be the required point.
Slope of the given line = \[-\] 2

\[\text { Since, the point lies on the curve } . \]

\[\text { Hence,} {y_1}^2 = 3 - 4 x_1 . . . \left( 1 \right)\]

\[\text { Now }, y^2 = 3 - 4x\]

\[ \Rightarrow 2y\frac{dy}{dx} = - 4\]

\[ \therefore \frac{dy}{dx} = \frac{- 4}{2y} = \frac{- 2}{y}\]

\[\text { Slope of the tangent } = \left( \frac{dy}{dx} \right)_\left( x_1 , y_1 \right) =\frac{- 2}{y_1}\]

\[\text { Given }:\]

\[\text { Slope of the tangent = Slope of the line }\]

\[ \Rightarrow \frac{- 2}{y_1} = - 2\]

\[ \Rightarrow y_1 = 1\]

\[\text { From (1), we get }\]

\[1 = 3 - 4 x_1 \]

\[ \Rightarrow - 2 = - 4 x_1 \]

\[ \Rightarrow x_1 = \frac{1}{2}\]

\[ \therefore \left( x_1 , y_1 \right) = \left( \frac{1}{2}, 1 \right)\]

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Solution for question: Find the Coordinates of the Point on the Curve Y2 = 3 − 4x Where Tangent is Parallel to the Line 2x + Y− 2 = 0 ? concept: Tangents and Normals. For the courses CBSE (Science), CBSE (Commerce), PUC Karnataka Science, CBSE (Arts)
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