Find the equation of the sphere which has centre at the origin and touches the line `2(x+1)=2-y=z+3.`

Find the equation of a sphere whose centre is (3,1,2) radius is 5.

Find the equation of the circle having center at (2,3) and which touches x+y=1

Find the equation of line which is normal to the parabola x^(2)=4y and touches the parabola y^(2)=12x .

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

Find the equation of a line which passes through the point (1,1,1) and intersects the lines (x-1)/2=(y-2)/3=(z-3)/4a n d(x+2)/1=(y-3)/2=(z+1)/4dot

Find the equations of the tangents to the curve y=(x+1)/(x-1) which are parallel to the line x + 2y = 6.

Find the joint equation of the pair of lines which pass through the origin and are perpendicular to the lines represented the equation y^2+3x y-6x+5y-14=0

Find the equation of the circle which touch the line 2x-y=1 at (1,1) and line 2x+y=4

Find the equation of the sphere which passes through (1,0,0),(0,1,0)a n d(0,0,1) and whose centre lies on the plane 3x-y+z=2.