The equation of the circle having centre at (3, −4) and touching the line \(5x + 12y - 12 = 0\) is ____.
\((x-3)^2 + (y+4)^2 = \left(\dfrac{45}{13}\right)^2\)
The equation of the circle circumscribing the triangle whose sides are the lines \(y = x + 2\), \(3y = 4x\), \(2y = 3x\) is ____.
\(x^2 + y^2 - 46x + 22y = 0\)
An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the length of the string and distance between the pins are ____.
Length of string = \(6 + 2\sqrt{5}\), distance between pins = \(2\sqrt{5}\).
The equation of the ellipse having foci \((0,1)\), \((0,-1)\) and minor axis of length 1 is ____.
\(4x^2 + \dfrac{4}{5}y^2 = 1\)
The equation of the parabola having focus at \((-1,-2)\) and the directrix \(x - 2y + 3 = 0\) is ____.
\(4x^2 + 4xy + y^2 + 4x + 32y + 16 = 0\)
The equation of the hyperbola with vertices at \((0, \pm 6)\) and eccentricity \(\dfrac{5}{3}\) is ____ and its foci are ____.
Equation: \(\dfrac{y^2}{36} - \dfrac{x^2}{64} = 1\). Foci: \((0, \pm 10)\).