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# a circle touches y-axis at (0,5) and whose centre lies on the lne 2x+y=13, find the equation of the circle

Grade:Select Grade

## 2 Answers

Vikas TU
14149 Points
3 years ago

A circle touching y-axis at (0,5) can be represented by
(0-h)^2 + ( 5 – k )^2 = r^2
• h^2 + ( 5 – k )^2 = r^2.
The circles center lies on 2x+y=13
• 2h + k = 13
But there would be many circles which has the center a=on that line and passes through (0,5).Hence there will be no single circle equation  if information about radius is not given.
Sagnnik Biswas
15 Points
2 years ago
As the circle touches y axis at (0,5) so we can write the center as (a, 5)
Now,  2x+y=13 contains the point (a, 5)
Or, 2a+5=13
Or a=4
Therefore,  center is (4,5)
Equation of circle will be,
(x-4)+(y-5)^2=16

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