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Solution for The Point on the Curve Y2 = X Where Tangent Makes 45° Angle with X-axis is (A) (1/2, 1/4) (B) (1/4, 1/2) (C) (4, 2)(D) (1, 1) - CBSE (Commerce) Class 12 - Mathematics

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Question

The point on the curve y2 = x where tangent makes 45° angle with x-axis is
(a) (1/2, 1/4)
(b) (1/4, 1/2)
(c) (4, 2)(d) (1, 1)

Solution

(b) (1/4, 1/2)
Let the required point be (x1, y1).
The tangent makes an angle of 45o with the x-axis.
∴ Slope of the tangent = tan 45o = 1

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

\[\text { Hence }, {y_1}^2 = x_1 \]

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

\[ \Rightarrow 2y\frac{dy}{dx} = 1\]

\[ \Rightarrow \frac{dy}{dx} = \frac{1}{2y}\]

\[\text { Slope of the tangent } = \left( \frac{dy}{dx} \right)_\left( x_1 , y_1 \right) =\frac{1}{2 y_1}\]

\[\text { Given }:\]

\[\frac{1}{2 y_1} = 1\]

\[ \Rightarrow 2 y_1 = 1\]

\[ \Rightarrow y_1 = \frac{1}{2}\]

\[\text { Now,} \]

\[ x_1 = {y_1}^2 = \left( \frac{1}{2} \right)^2 = \frac{1}{4}\]

\[ \therefore \left( x_1 , y_1 \right) = \left( \frac{1}{4}, \frac{1}{2} \right)\]

  Is there an error in this question or solution?
Solution for question: The Point on the Curve Y2 = X Where Tangent Makes 45° Angle with X-axis is (A) (1/2, 1/4) (B) (1/4, 1/2) (C) (4, 2)(D) (1, 1) concept: Tangents and Normals. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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