Question

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

Answer 1

Step-by-step explanation:

Centre 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 centre (1,2) to point (−1,0)

r2=(1+1)2+(2–0)2=8

Equation of circle:

(x−1)2+(y−2)2=8