Question

.
17. Find the equation of a circle of radius 5 which lies within the circle
x + y + 14x + 10y - 26 = 0 and which touches the given circle at the point (-1, 3).
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Answer 1

Step-by-step explanation:

x

2

+y

2

+14x+10y−26=0

r=

(7)

2

+(5)

2

−(−26)

=10

Other circle lies in the given circle and its radius is 5 , so it also passes through the centre of the given circle

Centre of given circle is (−7,−5)

Now we have the ends point of diameter of the other circle , so its centre is

(

2

−7−1

,

2

−5+3

)

(−4,−1)

r=5

So the equation of other circle is

(x+4)

2

+(y+1)

2

=5

2

x

2

+y

2

+8x+2y−8=0