Question

Find the distance between the points a(at1^2 2at1) and b(at2^2 2at2)

Answer 1

Given Co-ordinates of the Point,

A(x₁, y₁) = (at₁², 2at₁)

B(x₂,y₂) = (at₂², 2at₂)

Using the distance formula to calculate distance between the two given points A and B.

Distance = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Distance = $\sqrt{(at_2^2 - at_1^2)^2 + (2at_2 - 2at_1)^2}$

D² = a²(t₂² - t₁²)² + 4a²(t₂ - t₁)²

D² = a²(t₂ - t₁)² [(t₂ + t₁)² + 4]

D = a(t₂ - t₁)√[t₂² + t₁² + 2t₁t₂ + 4]

This is the required distance between these 2 co-ordinates.

Hope it helps.

Answer 2

Answer:

Given Co-ordinates of the Point,

A(x₁, y₁) = (at₁², 2at₁)

B(x₂,y₂) = (at₂², 2at₂)

Using the distance formula to calculate distance between the two given points A and B.

Distance =

Distance =

D² = a²(t₂² - t₁²)² + 4a²(t₂ - t₁)²

D² = a²(t₂ - t₁)² [(t₂ + t₁)² + 4]

D = a(t₂ - t₁)√[t₂² + t₁² + 2t₁t₂ + 4]

This is the required distance between these 2 co-ordinates.