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 - y1 = m(x - x1), Where m = slope
Calculation:
Here, y = 2x2
\(\rm \frac {dy}{dx}\) = 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.