Analytic Geometry Answers

Find the equation of the normal of the paraboloid 3x²+4z²+4y=0 at the point (2,-4,1). Also find the point where this line again intersects the paraboloid.

Find the equation of the cyclinder with base x²+y²+z²+3x+3y-z=1, x+y+2z=2.

Find the equation of the plane which passes through the line of intersection of the planes x+y-2z=1 and 2x+y-4z=3 and which is perpendicular to the plane x+y+z=1.

Find the equation of the tangent plane to the conicoid x²+y²=kz at the point (k,k,2k), where k is a constant. Represent the plane geometrically. Now take different values of k, including both positive and negative, and see how the shape of the conicoid changes.

Find the distance of the point of intersection of the line
x-2/1=y+3/-1=z/3
and the plane 2x-3y+4z+4=0 from the origin.

Identify and trace the conicoid y²+z²=x. Describe its sections by the planes x=0, y=0 and z=0.

Find the transformation of the equation 12x²-2y²+z²=2xy if the origin is kept fixed and the axes are rotated in such a way that the direction ratios of the new axes are 1,-3,0; 3,1,0; 0,0,1.

Find the equations of the spheres which pass through the circle x²+y²+z²=9, 2x+2y-7=0 and touch the plane x-y+z+3=0

Obtain the equation of the conic, a focus of which lies at (2,1), the directrix of which is x+y=0 and which passes through (1,4). Also identify the conic.

Q.Choose the correct answer.
Q. The equation 2x2+7y2-4xy+3y-1=0 represents
a. A pair of straight lines
b. Ellipse
c. Parabola
d. Hyperbola