Question

If ax+by=1 and cx^(2)+dy^(2)=1 have only one solution then show that (a^(2))/(c)+(b^(2))/(d)=1 and (i) x=(a)/(c) y=(b)/(d)​

Answer 1

Step-by-step explanation:

ax+by=1

diff. both sides

a+by*=0=>y*=-a/b

if cx²+dy²=1

diff both sides

2cx+2dyy*=0

cx+dy(-a/b)=0

bcx-ady=0

bcx=ady

x/y=ad/bc

x/y=(a/c)/(b/d)

comparing both sides if x=a/c thereforw y=b/d

putting values of x and y in any one eq

a(a/c) +b(b/d)=1

a²/c +b²/d =1