Question

SLOVE BY DISTANCE FORMULA

Q .no 1 ka 6th part ( circled one )

Answer 1

Note: Here, I am writing Alpha as a.

Given points are P(asina,acosa) and Q(acosa,-asina).

Distance between the two points PQ^2 = (x2 - x1)^2 + (y2 - y1)^2.

= > [(acosa - asina)]^2 + [(-asina - acosa)]^2

= > a^2cos^2a + a^2sin^2a - 2a^2cosasina + a^2sin^2a + a^2cos^2a + 2a^2sinacosa

= > a^2(cos^2a + sin^2a) + a^2(sin^2a + cos^2a)

= > a^2(1) + a^2(1)

= > 2a^2

$= > PQ = \sqrt{2}a$

Hope this helps!

Answer 2

We are asked to find the distance between the point P & Q,

P = ( asinα , acosα )
Q = ( acosα , -asinα )

We know that,
Distance between the points , $A(x_{1},y_{1} ) , B ( x_{1}, y_{2} )$ is $AB = \sqrt{(x_{2}-x_{1})^2 + (y_{2} - y_{1})^2 }$

Now,

PQ = √[ ( asinα-acosα)² + (acosα + asinα)² ]

= √ [ a²(sin²α+cos²α) - 2a² sinαcosα + a² ( sin²α + cos²α ) + 2a²sinαcosα ]

= √ a² + a²

= √2 a

Formulae used :

1) sin²A + cos²A = 1

2) ( a + b )² = a² + b² + 2ab

Hope helped!