" (5.) "ax+by=-p,ax-cy=q

If the three lines x-3y=p,ax+2y=q and ax+y=r from a right-angled triangle then:

[[a, b, ax + byb, c, bx + cyax + by, bx + cy, 0]] = (b ^ (2) -ac) (ax ^ (2) + 2bxy + cy ^ (2))

Prove that: |(a,b, ax+by),(b,c,bx+cy), (ax+by, bx+cy,0)|=(b^2-a c)(a x^2+2b x y+c y^2) .

Prove that |(a,b,ax+by),(b,c,bx+cy),(ax+by, bx + cy, 0)| = (b^(2)-ac)(ax^(2) + 2bxy + cy^(2)) .

If the circles x ^(2) +y^(2) +2ax+cy+a=0 and x ^(2) +y^(2) -3ax+dy-1=0 intersect in two distinic points P and Q, then the line 5x+by-a=0 passes through P and Q for-

If b^2 -aclt0 and alt 0, then thevalue of the determinant |(a,b,ax+by),(b,c,bx+cy),(ax + by,bx + cy,0)| is