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The extremities of a diameter of a circle having coordinates(-4,3) and (12,-1). What length does the circle intercept on y-axis.

The extremities of a diameter of a circle having coordinates(-4,3) and (12,-1). What length does the circle intercept on y-axis.
 

Grade:11

1 Answers

Susmita
425 Points
5 years ago
Let the circle has centre at (a,b) and radius r.
Then equation of circle is
(x-a)2+(y-b)2=r2
Now the centre divides the diameter in 1:1 ratio.By using section formula find out the coordinate of the centre as follows:
a=(-4+12)/2=8/2=4
and b=(3-1)/2=2/2=1
Radius is the distance between any of the points and centre.Let us take (-4,3) and (4,1).So
r2=(-4-4)2+(3-1)2=64+4=68
So the equation of circle becomes
(x-4)2+(y-1)2=68 •••••(1)
y intercept means x=0.putting x=0 in eq(1)
16+(y-1)2=68
Or,(y-1)2=52
Or,(y-1)=\pm \sqrt{52}
Or,y=\pm \sqrt{52}+1
Or,y1=\sqrt{52}+1 and Or,y2=-\sqrt{52}+1
So length of y intercept is
Or,y1-y2=2 \sqrt{52}
Hope this helps.

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