Question

Find the equation of the circle passing through (-1,0)and touching x+y-7 =0 at (3,4)

Answer 1

Answer:

(x−1)2+(y−2)2=8

Step-by-step explanation:

Center of circle  =(h,k)  

Line  x+y−7=0  has slope  =−1 . Since circle touches line at  (3,4) , then slope from  (h,k)  to  (3,4)=1  

k−4h−3=1  

k=h+1  

Distance from point  (h,k)  to point  (−1,0)  = distance from  (h,k)  to line  x+y−7=0  

(h+1)2+(k−0)2−−−−−−−−−−−−−−−√=|h+k−7|12+12−−−−−−√  

(h+1)2+(h+1)2=(h+(h+1)−7)22  

4(h+1)2=(2h−6)2  

2(h+1)=±(2h−6)  

h=1  

k=2  

Radius is distance from center  (1,2)  to point  (−1,0)  

r2=(1+1)2+(2–0)2=8  

Equation of circle:

(x−1)2+(y−2)2=8

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Answer 2

Answer:

shokfaflogdfhlkfdg2369993#_:"$39933569

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