Question

Solve p² +q² = 1, Solution is a)) z = ax + √1 + a²y+c c) z = ax + √1-a²y + c b) z = ax - √1-a²y + c d) z = ax - √1 + a²y + c

Answer 1

Answer:

Let F=px+qy+p2+q2=0F=px+qy+p2+q2=0. Then by Charpit's auxiliary equations

dpFx+pFz=dqFy+qFz=dz−pFp−qFq=dx−Fp=dy−FqdpFx+pFz=dqFy+qFz=dz−pFp−qFq=dx−Fp=dy−Fq

we have

dp0=dq0=dz−p(x+2p)−q(y