Grade 11Analytical Geometry

Find the equation of the circle which is concentric with the circle x^2 + y ^2 - 2x - 6y - 3= 0 and passes through the point of intersection of the lines 2x + 3y =1 and x - y = 3

Sagar saha

6 Years agoGrade 11

1 Answer

Aditya Gupta

6 Years ago

observe that point of intersection of the lines 2x + 3y =1 and x - y = 3 can found out by solving these eqns together, to obtain (2, – 1).

now, x^2 + y ^2 - 2x - 6y - 3= 0 can be written as (x – 1)^2 + (y – 3)^2= 13, so its centre is (1, 3).

as the other circle is conentric with this circle, it too will have the same centre. so its eqn is:

(x – 1)^2 + (y – 3)^2= r^2, where r is its radius. but, it passes through point of intersection of the lines 2x + 3y =1 and x - y = 3, which is (2, – 1).

so, (2 – 1)^2 + ( – 1 – 3)^2= r^2

or r^2= 17

hence eqn becomes

(x – 1)^2 + (y – 3)^2= 17

or x^2 + y^2 – 2x – 6y – 7= 0

kindly approve :))

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Find the equation of the circle which is concentric with the circle x^2 + y ^2 - 2x - 6y - 3= 0 and passes through the point of intersection of the lines 2x + 3y =1 and x - y = 3

Sagar saha

1 Answer

Aditya Gupta

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