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Tangents and Normals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSTangents and Normals1 Mark
MCQ
The normal at the point $(1, 1)$ on the curve $2y + x^2 = 3$ is:
  • A
    $x + y = 0$
  • ✓
    $x - y = 0$
  • C
    $x + y + 1 = 0$
  • D
    $x - y = 1$
✓

Answer

Correct option: B.
$x - y = 0$
$2y + x^2 = 3$
$2\frac{\text{dy}}{\text{dx}}+2\text{x}=0$
$\frac{\text{dy}}{\text{dx}}=-\text{x}$
$\Big(\frac{\text{dy}}{\text{dx}}\Big)_{(1,1)}=-1$
Slope of the normal $= 1$
Equation of the normal
$y - 1 = x - 1$
$y = x$
$x - y = 0$

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