A triangle has two of its sides along the axes, its third side touches the circle : `x^2+y^2-2ax-2ay+a^2=0, (a!=0)`

A triangle has two of its sides along the axes, its third side touches the circle x^2 + y^2 -2ax-2ay+a^2=0 . Find the equation of the locus of the circumcentre of the triangle.

Find the centre and radius of the circles : x^2 + y^2 - ax - by = 0

The circle x^2+y^2-4x-4y+4=0 is inscribed in a triangle which has two of its sides along the coordinate axes. The locus of the circumcenter of the triangle is x+y-x y+k(x^2+y^2)^(1/2)=0 . Find kdot

A triangle has two of its sides along the lines y=m_1x&y=m_2x where m_1, m_2 are the roots of the equation 3x^2+10 x+1=0 and H(6,2) be the orthocentre of the triangle. If the equation of the third side of the triangle is a x+b y+1=0 , then a=3 (b) b=1 (c) a=4 (d) b=-2

A triangle has two of its sides along the lines y=m_1x&y=m_2x where m_1, m_2 are the roots of the equation 3x^2+10 x+1=0 and H(6,2) be the orthocentre of the triangle. If the equation of the third side of the triangle is a x+b y+1=0 , then a=3 (b) b=1 (c) a=4 (d) b=-2

A triangle has two of its vertices at (0,1) and (2,2) in the cartesian plane. Its third vertex lies on the x-axis. If the area of the triangle is 2 square units then the sum of the possible abscissae of the third vertex, is-

Find the locus of the circumcenter of a triangle whose two sides are along the coordinate axes and the third side passes through the point of intersection of the line a x+b y+c=0 and l x+m y+n=0.

If a triangle is inscribed in an ellipse and two of its sides are parallel to the given straight lines, then prove that the third side touches the fixed ellipse.

Show that the angle between the circles x^2+y^2=a^2, x^2+y^2=ax+ay is (3pi)/4

The line ax+by+by+c=0 is normal to the circle x^(2)+y^(2)+2gx+2fy+d=0, if