Question

can any help me on this question??

The radius of circle x²+ y²-2x+3y+k=0 is 2½. Find the value of k.Find also the equation of diameter of the circle , which passes through the point (5,2½)​

Answer 1

k = - 3 if the radius of circle x² + y² - 2x  + 3y  + k   =0 is 5/2

2x - 2y = 5  is equation of diameter of the circle which passes through the point (5,5/2)​

Step-by-step explanation:

x² + y² - 2x  + 3y  + k   =0

=> (x - 1)² - 1  +  ( y  + (3/2))²  - 9/4 + k = 0

=> (x - 1)² + (y  + 3/2)² = 13/4 - k

Center of Circle =  1 , - 3/2

radius = √(13/4 - k)

=> 13/4 - k = (5/2)²

=> 13/4 - k = 25/4

=> k = - 3

Diameter will Pass through center & also passing through (5 , 5/2)

slope  =  (5/2 -(-3/2))/(5 -1)

= 4/4

= 1

y = x + c

5/2 = 5 + c

=> c = -5/2

=> y = x - 5/2

=> 2y = 2x - 5

=> 2x - 2y= 5