Question

A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line, y4x+3=0, then its radius is equal to

Answer 1

Answer:

Its radius is : r = 2.

Step-by-step explanation:

We know that the equation of a circle is:

( x - p )²  + ( y - q )² = r², so:

( 2 - p )² + ( 3 - q )² = r²

( 4 - p )² + ( 5 - q )² = r²

--------------------------------

4 - 4 p + p² + 9 - 6 q + q² = r²

16 - 8 p + p² + 25 - 10 q + q² = r²  /* (-1)

-----------------------------------------------------

4 - 4 p + p² + 9 - 6 q + q² = r²

                                            +

- 16 + 8 p - p² - 25 + 10 q - q² = r²

-------------------------------------------------

4 p + 4 q = 28  , and we know that a center lies on the line:

- 4p + q = -3

5 q = 25,  q = 25 : 5,  q = 5,  p = 2

We will put it into the first equation:

( 2 - 2 )² + ( 3 - 5 )² = r²

r² = 4

r = 2.