Find the equation of the circle passing through the points (1, 1 ), (2, -1 ) and (3, 2) .

 A road bridge over an irrigation canal have two semi circular vents each with a span of 20m and the supporting pillars of width 2m. Use Figure to write the equations that represents the semi-verticular vents

Find the equations of tangents to the hyperbola \(\frac { { x }^{ 2 } }{ 16 } -\frac { { y }^{ 2 } }{ 64 } \) = 1 which are parallel to10x − 3y + 9 = 0.

Show that the line x−y+4 = 0 is a tangent to the ellipse x²+3y² = 12 . Also find the coordinates of the point of contact.

The maximum and minimum distances of the Earth from the Sun respectively are 152 × 10⁶ km and 94.5 × 10⁶ km. The Sun is at one focus of the elliptical orbit. Find the distance from the Sun to the other focus.