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find eqn of circle touching the Yaxis at a distance-3 from origin and intercepting a length 8 on the X axis
Asked by mohitraj54085 | 29 Feb, 2024, 06:27: PM
Expert Answer
Figure shows a circle that touches the y -axis at D and makes intercept AB at y-axis.
We are given that OD = 3 unit and AB = 8 unit .
Let C be the centre of circle and CE is perpendicular to chord AB .
Hence we get , AE = BE = 4 unit
CE = OD = 3 unit
Hence AC = 5 unit
Hence AC is radius of circle , DC= AC = 5 unit
Hence center coordinate of circle is C ( 5, 3 )
If center is (h, k ) and radius of circle is r , then equation of circle is
(x-h)2 + ( y - k )2 = r2
hence equation of circle that has centre at ( 5, 3 ) and radius 5 unit is
(x-5)2 + (y - 3)2 = 52
Hence, equation of circle is x2 + y2 -10x - 6y + 9 = 0
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