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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

#### 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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#### Video TutorialsVIEW ALL [3]

Solution 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.
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