Tangents and Normals — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsTangents and Normals3 Marks
Question
Write the angle between the curves y2 = 4x and x2 = 2y - 3 at the point (1, 2).
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Answer
Given: y2 = 4x ...(1) x2 = 2y − 3 ...(2) On differentiating (1) w.r.t.x, we get $2\text{y}\frac{\text{dy}}{\text{dx}}=4$ $\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{2}{\text{y}}$ $\Rightarrow\text{m}_1=\Big(\frac{\text{dy}}{\text{dx}}\Big)_{(1,2)}=\frac{2}{2}=1$ On differentiating (2) w.r.t.x, we get $2\text{x}=2\frac{\text{dy}}{\text{dx}}$ $\Rightarrow\frac{\text{dy}}{\text{dx}}=\text{x}$ $\Rightarrow\text{m}_2=\Big(\frac{\text{dy}}{\text{dx}}\Big)_{(1,2)}=1$ Thus, we get $\tan\theta=\Big|\frac{\text{m}_1-\text{m}_2}{1+\text{m}_1\text{m}_2}\Big|$ $\Rightarrow\tan\theta=\Big|\frac{1-1}{1+1}\Big|$ $\Rightarrow\tan\theta=0$ $\Rightarrow\theta=0$
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