Question

the length of the chords of the circle X square + Y square equal to 25 passing through 50 and perpendicular to the line X + Y is equal to zero

Answer 1

Length of Chord =  5√2   if Chord  of  x² + y²  = 25 passing through 5,0 and  perpendicular to the line x + y = 0

Step-by-step explanation:

x² + y²  = 25

=> x² + y² = 5²

Center = (0,0)  radius = 5

Line ⊥ x + y = 0

would be y  = x + c

passing through ( 5 , 0)

=> 0 = 5 + c

=> c = -5

=> y = x - 5

putting in  x² + y²  = 25

=> x²+ (x - 5)² = 25

=> x² + x² + 25 - 10x = 25

=> 2x² - 10x = 0

=> x² - 5x = 0

=> x(x - 5) = 0

=> x = 0 or 5

  y = -5  , 0

Two points of chord

(5 , 0)  &  ( 0, 5)

Length of Chord = √5² + 5² = 5√2  

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