Analytic Geometry Answers

Obtain eqñ of parabola with focus(3,2)
Directrix 3x-4y+9=0

a) Obtain the equation of the parabola with focus )2,3( and directrix
3x − 4y + 9 =

Find the radius and the center of the circular section of the sphere jrj = 26 cut off
by the plane r
(2i+6j+3k) = 70.

1. The sides of a triangle are given by the equations 2x + y = 5, x + 2y = 7 and
x - y = 1 find the vertices of the triangle and illustrate with a sketch.

2. Show that the three lines given by the equations 3x + 5y + 7 = 0, x + 2y + 2 = 0 and 2x - y + 9 =0 are concurrent (i. e. Pass through the one point)

1. Find the point of intersection of the following pairs of linea whose equations are given.
a) x + 3y = 9 and 5x - 2y = 11
b) 4x + 3y =8 and 6x - 2y = - 14
c) 3x + 2y - 7 =0 and 5x - 6y = 7

2. Find the equation of the straight line which passes through the origin and through the point of intersection of the lines 4x - y- 3 =0 and x + 2y - 12=0

Find the distance of the centre of the circle x^2+y^2+z^2+x-2y+2z=3, 2x+y+2z=1 from the plane ax+by+cz=d where a,b,c,d are constants and also find the equation of the right circular cylinder whose base curve is the circle obtained above.
above.

Can any conic have its focus lying on the corresponding directrix? Give reasons for
your answer.

Identify an axis of revolution and generating conic of the surface 4x^2+25y^2+4z^2=100. Does this conic also generate x^2/4 + y^2/25 + z^2/4=1?Give reasons for your answer.

A rotating liquid forms a surface in the form of a paraboloid. The surface is 2m
deep at the centre and 10m across. Obtain an equation of the surface.

Find the equation of the conic of which one focus lies at (2,1) one directrix is
x + y = 0 and it passes through (1,4) Also identify the conic and reduce the conic you obtained above to standard form.
Draw a rough sketch of the conic obtained above.