[y^(2)-4ax,=0],[" JPT "55." &m ",p^(2)+2py cot x-y^(2)=0]

Abscissas and ordinates of points A and B are roots of equation x^(2) + 2ax - b^(2) = 0 " and " y^(2) + 2py - q^(2) = 0 respectively. Equation of circle with AB as a diameter is

Solve p^(2)+2py cot x=y^(2), where p=(dy)/(dx)

The locus of the point (l, m) so that lx+my=1 touches the circle x^(2)+y^(2)=a^(2) is :a) x^(2)+y^(2)-ax=0 b) x^(2)+y^(2)=1/a^(2) c) y^(2)=4ax d) x^(2)+y^(2)-ax-ay+a^(2)=0

The locus of a point "P" ,if the join of the points (2,3) and (-1,5) subtends right angle at "P" is x^(2)+y^(2)-x-8y+13=0 x^(2)-y^(2)-x+8y+3=0 x^(2)+y^(2)-4x-4y=0,(x,y)!=(0,4)&(4,0) x^(2)+y^(2)-x-8y+13=0,(x,y)!=(2,3)&(-1,5)

The least distance between two points P and Q on the circle x^(2) + y^(2) -8x + 10y + 37 =0 and x^(2) + y^(2) + 16x + 55 = 0 is _______ .

The least distance between two points P and Q on the circle x^(2) + y^(2) -8x + 10y + 37 =0 and x^(2) + y^(2) + 16x + 55 = 0 is _______ .

If the intersection point of the straight lines represented by ^(2)-2ax+8y+c=0 is x^(2)+2xy+4y^(2)-2ax+8y+c=0 is (1,-(5)/(4)), then

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

Find the centre and radius of each of the following circle : (i) x^(2)+y^(2)+4x-4y+1=0 (ii) 2x^(2)+2y^(2)-6x+6y+1=0 (iii) 2x^(2)+2y^(2)=3k(x+k) (iv) 3x^(2)+3y^(2)-5x-6y+4=0 (v) x^(2)+y^(2)-2ax-2by+a^(2)=0