Question

class 10th
chapter 9 (co-ordinate geometry) ​

Answer 1

Answer:

Step-by-step explanation:

The formula for distance between two points (x₁, y₁) and (x₂, y₂) is

√ [(x₂ - x₁)² + (y₂ - y₁)²]

So Distance between points (at₁², 2at₁) and (at₂², 2at₂) is

√ [(at₂² - at₁²)² + (2at₂ - 2at₁)²]

= √[a²(t₂² - t₁²)² + 4a²(t₂ - t₁)²]

//t₂² - t₁² is of form a² - b², thus  t₂² - t₁² = (t₂ - t₁)(t₂ + t₁)

= √ [a²{(t₂ - t₁)(t₂ + t₁)}²  + 4a²(t₂ - t₁)²]

= √ [a²{(t₂ - t₁)²(t₂ + t₁)²} + + 4a²(t₂ - t₁)²]

//a²(t₂ - t₁)² is common

= √ [ a²(t₂ - t₁)² {(t₂ + t₁)² + 4} ]

//Bring out a²(t₂ - t₁)² out of the square root which becomes a(t₂ - t₁)

= a(t₂ - t₁) √[(t₂ + t₁)² + 4]