Question

A tangent touches the parabola y² = -8x at the point (-2, 4) then the slope of the tangent is ?
1. -2
2. 2
3. -1
4. 1

Answer 1

Correct Answer - Option 3 : -1

Concept:

The equation of tangent at (x₁, y₁) can also be obtained by replacing x² by xx₁, y² by yy₁,x by (x + x₁)/2, y by(y + y₁)/2 and xy by (xy₁ + x₁y)/2 and without changing the constant in the equation of curve. 

Calculation:

Given equation of parabola is  y2 = -8x.

Equation of parabola at point (x1, y1),  yy₁ = -8(x + x₁)/2

⇒ Equation of parabola at point (-2, 4),  4y = -8(x + (-2))/2

⇒  4y = -4(x - 2)

⇒  y = - (x - 2)

⇒  y = - x + 2

Comparing it with y = mx + c we get

Slope of tangent = m = -1.

Hence, option 3 is correct.