" (ix) "3a^(2)y^(2)-aby=2b^(2),a!=0

Factorise the using the identity a ^(2) - 2 ab + b ^(2) = (a -b) ^(2). a ^(2) y ^(2) - 2 aby + b ^(2)

The polar of the line ax+by+3a^(2)+3b^(2)=0 w.r.t. to the circle x^(2)+y^(2)+2ax+2by-a^(2)-b^(2)=0 is

Factorise the using the identity a ^(2) - 2 ab + b ^(2) = (a -b) ^(2). a ^(2) y ^(3) - 2 aby ^(2) + b ^(2) y

If a circle passes through the point (a, b) and cuts the circle x^2 + y^2 = 4 orthogonally, then the locus of its centre is (a) 2ax+2by-(a^(2)+b^(2)+4)=0 (b) 2ax+2by-(a^(2)-b^(2)+k^(2))=0 (c) x^(2)+y^(2)-3ax-4by+(a^(2)+b^(2)-k^(2))=0 (d) x^(2)+y^(2)-2ax-3by+(a^(2)-b^(2)-k^(2))=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

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 radius of the circle sqrt(1 + a^(2)) (x^(2) + y^(2)) - 2bx - 2aby = 0 is

Locus of centroid of the triangle whose vertices are (a cos t,a sin t),(b sin t-b cos t)and(1,0) where t is a parameter is: (3x-1)^(2)+(3y)^(2)=a^(2)-b^(2)(3x-1)^(2)+(3y)^(2)=a^(2)+b^(2)(3x+1)^(2)+(3y)^(2)=a^(2)+b^(2)(3x+1)^(2)+(3y)^(2)=a^(2)-b^(2)

If y=Pe^(ax)+Qe^(bx) , show that : (d^(2)y)/(dx^(2))-(a+b)dy/dx+aby=0 .

If y="Pe"^(ax)+"Qe"^(bx) , then show that (d^(2)y)/(dx^(2))-(a+b)(dy)/(dx)+aby=0