Question

The line y = 2x + b is a tangent to the parabola y² = 8x, if:
1. \(b = \frac 1 2\)
2. b = 2
3. b = -1
4. b = 1

Answer 1

Correct Answer - Option 4 : b = 1

Concept:

Equation of parabola	Point of contact in terms of slope (m)	Equation of tangent in terms of slope	Condition of tangency
\({y^2} = 4ax\)	\(\left( {\frac{a}{{{m^2}}},\;\frac{{2a}}{m}} \right)\)	\(y = mx + \frac{a}{m}\)	\(c = \frac{a}{m}\)

 

Analysis:

The equation of tangent is:

y = 2x + b

Comparing with \(y = mx + \frac{a}{m}\) we get:

m = 2, a/m = b

The equation of the parabola is:

y2 = 8x

4a = 8, a = 2

∴ a/m = 1/1 = 1

The condition of tangency:

b = 1