Question

find the distance between the following point:

Answer 1

Is it question of clas 10 ....??

Answer 2

$\huge \underline \mathfrak {Solution:-}$

We have to find out the distance between the two points (at1^2,2at1) and (at2^2,2at2).

For finding the distance between two points we can use the given formula.

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

This formula is used to find out the distance between two points and that's why it is named as distance formula.

According to question,

$x_1 ={at_1}^{2} \\ \\ y_1= 2at_1 \\ \\ x_2= {at_2}^{2} \\ \\ y_2 = 2at_2$

Now,

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

$= \sqrt{ {( at_1^{2}-at_2^{2})}^{2} + {( 2at_1 - 2at_2)}^{2} } \\ \\ = \sqrt{ {(a( t_1^{2}-t_2^{2}))}^{2} + { 4(at_1^{2}-at_2^{2})}^{2} } units$

So, it is the distance between the points .