`(a+b)^2x^2-4a b x-(a-b)^2=0`

Solve by factorization: 4x^2+4b x-(a^2-b^2)=0

If =|-x a bb-x a a b-x| , then a factor is a+b+x x^2-(a-b)+x+a^2+b^2+a b x^2-(a+b)+x+a^2+b^2-a b a+b-x

If =|-x a bb-x a a b-x| , then a factor is a+b+x x^2-(a-b)+x+a^2+b^2+a b x^2-(a+b)+x+a^2+b^2-a b a+b-x

The locus of the midpoints of the chords of the circle x^2+y^2-a x-b y=0 which subtend a right angle at (a/2, b/2) is (a) a x+b y=0 (b) a x+b y=a^2+b^2 (c) x^2+y^2-a x-b y+(a^2+b^2)/8=0 (d) x^2+y^2-a x-b y-(a^2+b^2)/8=0

The locus of the midpoints of the chords of the circle x^2+y^2-a x-b y=0 which subtend a right angle at (a/2, b/2) is (a) a x+b y=0 (b) a x+b y=a^2=b^2 (c) x^2+y^2-a x-b y+(a^2+b^2)/8=0 (d) x^2+y^2-a x-b y-(a^2+b^2)/8=0

If two distnct chords of the circle x^2+y^2 -2x -4y=0 drawn from the point P (a,b) are bisected by y-axis then a) (b+2)^2>4a b) (b-2)^2>4a c) (b-2)^2>2a d) (b+2)^2>a

Solve by factorization: 9x^2-6b^2x-(a^4-b^4)=0

If x = (sqrt(a^2+b^2)+sqrt(a^2-b^2))/(sqrt(a^2+b^2)-sqrt(a^2-b^2)) show that b^2x^2-2a^2x+b^2 =0 .

If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.

If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.