Question

the centre of a circle is (2 p - 1, 2p - 2 )if a circle passes through the point A (1,2) and the length of its diameter is 20 units find p.

Answer 1

HELLO DEAR,


GIVEN THAT:-

Diameter :- 20 units .

Radius :- 10 units .

A ( 1 , 2 ) , O ( 2p - 1 , 2p - 2 ) .

AO = 10 units .

To find :- p = ?

Solution ;-

By distance formula :-

$\sqrt{(2p - 1 - 1)^{2} + (2p - 2 - 2)^{2} } = 10 \\ = > \sqrt{4 {p}^{2} + 4 - 8p + 4{p}^{2} + 16 - 16p} = 10$
Squaring on both sides ;-

8p2 - 24p + 20 = 100

8p2 - 24p + 20 - 100 = 0

8p2 - 24p - 80 = 0

p2 - 3p - 10 = 0

By using quadratic formula 

Let p = x .

THEN ,


X²- 5X + 2X - 10


=> X(X-5) +2(X-5)

(X+2) (X-5)=0

THEN X=5 &X=-2


I HOPE ITS HELP YOU DEAR,

THANKS

Answer 2

Diameter :- 20 units .

Radius :- 10 units .

A ( 1 , 2 ) , O ( 2p - 1 , 2p - 2 ) .

AO = 10 units .

To find :- p = ?

Solution ;-

By distance formula :-


Squaring on both sides ;-

8p2 - 24p + 20 = 100

8p2 - 24p + 20 - 100 = 0

8p2 - 24p - 80 = 0

p2 - 3p - 10 = 0

By using quadratic formula 

Let p = x .

THEN ,


X²- 5X + 2X - 10


=> X(X-5) +2(X-5)

(X+2) (X-5)=0

THEN X=5 &X=-2√