Find the equation of the circle described on the line segment joining the foci of the parabolas `x^2 - 4ay and y^2 = 4a(x-a)` as diameter.

Equation of the line joining the foci of the parabola y^(2)=4x and x^(2) = -4y is

Let P_(1) : y^(2) = 4ax and P_(2) : y^(2) =-4ax be two parabolas and L : y = x be a straight line. if a = 4, then the equation of the ellipse having the line segment joining the foci of the parabolas P_(1) and P_(2) as the major axis and eccentricity equal to (1)/(2) is

The equation of the circle described on the common chord of the circles x^(2)+y^(2)-4x-5=0 and x^(2)+y^(2)+8y+7=0 as a diameter,is

Show that the equation of the circle described on the chord intercepted by the parabola y^(2)=4ax on the line y=max+c as diameter is m^(2)(x^(2)+y^(2))+2x(mc-2a)-4amy+4amc+c^(2)=0

The circle drawn on the line segment joining the foci of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 as diameter cuts the asymptotes at (A) (a,a) (b) (b,a)(C)(+-b,+-a)(D)(+-a,+-b)

Find the area common to two parabolas x^(2)=4ay and y^(2)=4ax, using integration.

A circle is described on the line joining the points (2,-3) and (-4,7) as a diameter, Find the equation of circle.

Find the equation of the circle the end points of whose diameter are the centres of the circle : x^2 + y^2 + 6x - 14y=1 and x^2 + y^2 - 4x + 10y=2 .

Equation of the circle of minimum radius which touches both the parabolas y=x^(2)+2x+4 and x-y^(2)+2y+4 is