Question

Prove that the tangents to the curve , y =
x²- 5x + 6 at the points (2,0) and (3,0) are at right angles.

Answer 1

To prove : the tangents to the curve , y = x² - 5x + 6 at the points (2,0) and (3,0) are at right angle.

solution : slope of tangent of curve, dy/dx = d(x² - 5x + 6)/dx

= 2x - 5

at (2,0) , slope of tangent , m₁ = 2 × 2 - 5 = -1

at (3,0), slope of tangent, m₂ = 2 × 3 - 5 = 1

we know, two lines are perpendicular only when products of slopes of lines = -1

i.e., m₁ × m₂ = -1

LHS = m₁ × m₂ = -1 × 1 = -1 = RHS

Therefore tangents at the points (2,0) and (3,0) are at right angle.

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Answer 2

Answer:

Step-by-step explanation:

Slope of tangent to curve y=dy/dx

Here,dy/dx=2x-5

At(2,0):dy/dx=(2*2)-5=-1

At(3,0):dy/dx=(2*3)-1=1

Two lines are perpendicular if product of slopes is -1.

Here,we get product as -1 (1*-1).

Hence,tangents to curve are at right angles.

Hope you understood