Analytic Geometry Answers

Find the equation of the normal to the curve y = x^3 - x^2 at point (1,1)

show that the points (-1, -2),(5,4),(-3,0) are the vertices of a right triangle, and find its area.

A line AB passes through the point P(3,-2) with gradient 2, determine the equation of the line CD through P perpendicular to AB.

Find the equations of those tangent planes to the sphere x^2+y^2+Z^2+2x-4y+6z-7=0 which intersect in the line 6x-3y-23=0,3z+2=0

and

Under what conditions on α do the spheres x^2 + y^2+ z^2+x+2z+1=0 intersect each other at an angle of 45 degree ?

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.