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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.


2 years ago

Susmita
425 Points
							Let the circle has centre at (a,b) and radius r.Then equation of circle is(x-a)2+(y-b)2=r2Now 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=4and b=(3-1)/2=2/2=1Radius is the distance between any of the points and centre.Let us take (-4,3) and (4,1).Sor2=(-4-4)2+(3-1)2=64+4=68So 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=68Or,(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.

2 years ago
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• Mind Map
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• NCERT Solutions
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