The orthocentre of triangle formed by the lines x + 3y = 10 and 6x² + xy - y² = 0 is:

B and C are two points on the circle x²+y²=a². From a point A(b, c) on that circle AB=AC=d. The equation to Bc is

The locus of the centre of the circles which touché both the circles x²+y²=a² and x²+y²=4ax externally has the equation

The equation of the circle belonging to the coaxal system of which (1, 2)(4, 3) are the limiting points and passing through the origin is

The length of the intercept made by the circle x²+y²+10x-12y-13=0 on y-axis is

The angle between a pair-of tangents drawn from a point P to the circle x²+y²+4x-6y+9sin²α+13cos² α=0 is 2α.The  equation of the locus of the point P is

The equation of the circle with centre at (-3, 4) and touching y-axis is

The centre of the circle (1+m²)(x²+y²)-2cx-2cmy=0 is

The equation of the circle which cuts orthogonally the  three circles x²+y²+4x+2y+1=0, 2x²+2y²+8x+6y-3=0 , x²+y²+6x-2y-3=0 is

If the lines 3x-4y-7 =0and 2x-3y-5=0 are two diameters of a circle of area 49π sq unit. Then the equation of this circle is