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if y=2x is a chord of the circle x^2+y^2-10x=0,find the equation of the circle with this chord as diameter.Hence find the length of the chord intercepted. PLEASE SHOW ALL THE STEPS

if y=2x is a chord of the circle x^2+y^2-10x=0,find the equation of the circle with this chord as diameter.Hence find the length of the chord intercepted.
 
 
PLEASE SHOW ALL THE STEPS

Grade:11

1 Answers

Arun
25763 Points
2 years ago
x² + 4x² - 10x = 0 
5x² - 10x = 0 
(5x) (x - 2) = 0 
x = 0 , x = 2 
y = 0 , y = 4 

End points of diameter (chord) are (0,0) and (2,4) 
Centre (1 , 2) 
r² = 1² + 2x² = 5 
r = √ 5 

[ x - 1 ]² + [ y - 2 ]² = 5

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