Correct Answer - Option 4 : x + 4y - 9 = 0

**Concept:**

**Slope of tangent to the curve = \(\rm \frac {dy}{dx}\)**

**Slope of normal to the curve** = \(\rm \frac{-1}{\left(\frac {dy}{dx}\right)}\)

**Point-slope** is the general form: y - y_{1} = m(x - x_{1}), Where m = slope

**Calculation:**

Here, y = 2x^{2}

\(\rm \frac {dy}{dx}\) = 4x

\(\rm \left.\frac{dy}{dx}\right|_{x=1}=4\)

Slope of normal to the curve =\(\rm \frac{-1}{\left(\frac {dy}{dx}\right)}\) = -1/4

Equation of normal to curve passing through (1, 2) is y - 2 = -1/4(x - 1)

⇒ 4y - 8 = -x + 1

⇒ x + 4y - 9 = 0

Hence, option (4) is correct.