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# Solution for The Angle Between the Curves Y2 = X and X2 = Y at (1, 1) is (A) Tan − 1 4 3 (B) Tan − 1 3 4 (C) 90° (D) 45° - CBSE (Commerce) Class 12 - Mathematics

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#### Question

The angle between the curves y2 = x and x2 = y at (1, 1) is
(a) $\tan^{- 1} \frac{4}{3}$

(b)$\tan^{- 1} \frac{3}{4}$

(c) 90°
(d) 45°

#### Solution

(b) $\tan^{- 1} \frac{3}{4}$

$\text { Given }:$

$y^2 = x . . . \left( 1 \right)$

$x^2 = y . . . \left( 2 \right)$

$\text { Point} = \left( 1, 1 \right)$

$\text { On differentiating (1) w.r.t.x, we get }$

$2y \frac{dy}{dx} = 1$

$\Rightarrow \frac{dy}{dx} = \frac{1}{2y}$

$\Rightarrow m_1 = \frac{1}{2}$

$\text { On differentiating (2) w.r.t.x, we get }$

$2x = \frac{dy}{dx}$

$\Rightarrow m_2 = 2\left( 1 \right) = 2$

$\text { Now,}$

$\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right| = \left| \frac{\frac{1}{2} - 2}{1 + \frac{1}{2} \times 2} \right| = \frac{3}{4}$

$\Rightarrow \theta = \tan^{- 1} \left( \frac{3}{4} \right)$

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#### Video TutorialsVIEW ALL [3]

Solution The Angle Between the Curves Y2 = X and X2 = Y at (1, 1) is (A) Tan − 1 4 3 (B) Tan − 1 3 4 (C) 90° (D) 45° Concept: Tangents and Normals.
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