Question

Find the equation of the circle in standard form: Tangent to the line x + 2y = 8 at (0,4) and passing through (3,7). (x − 1)^2 + (y − 6)^2 = 5.


nonsense=report

Answer 1

Explanation:

Centre lies on the line y−4x+3=0

Let x=h

⇒y=4h−3

So the center is of the form (h,4h−3)

Distance of centre from (2,3) and (4,5) will be equal

⇒(h−2)

2

+(4h−3−3)

2

=(h−4)

2

+(4h−3−5)

2

⇒h=2

So the centre is (2,5)

r=

(2−2)

2

+(5−3)

2

=2

So the equation of the circle is

(x−2)

2

+(y−5)

2

=2

2

x

2

+y

2

−4x−10y+25=0