The ellipse `4x^2+9y^2=36` and the hyperbola `a^2x^2-y^2=4` intersect at right angles. Then the equation of the circle through the points of intersection of two conics is

The ellipse 4x^(2) + 9y^(2) = 36 and the hyperbola 4x^(2) – y^(2) = 4 have the same foci and they intersect at right angles then the equation of the circle through the points of intersection of two conics is

The equation of the line through the intersection of the lines 2x-3y=0 and 4x-5y=2 and

The circle x^(2)+y^(2)8x=0 and hyperbola (x^(2))/(9)(y^(2))/(4)=1 intersect at points A and B .Then Equation of the circle with A B as its diameter is

The circle x^(2)+y^(2)-8x=0 and hyperbola (x^(2))/(9)-(y^(2))/(4)=1 intersect at the points A and B Equation of the circle with AB as its diameter is

The circle x^(2)+y^(2)-8x=0 and hyperbola (x^(2))/(9)-(y^(2))/(4)=1 intersect at the points A and B . The equation of a common tangent with positive slope to the circle as well as to the hyperbola, is

The parabola y^(2)=4x and the circle having its center at (6,5) intersect at right angle.Then find the possible points of intersection of these curves.

Find the equation of the circle passing through the point (2, 4) and centre at the point of intersection of the lines x-y=4 and 2x+3y=-7 .