Analytic Geometry Answers

find the general equation of a line parallel to the line 2x+3y-6=0 and passing at a distance 5 square root 13 over 13 from the point (-1,1)

Identify the concoid 1+2x^2+9y^2=3z^2. Does the XY plane intersect with it? Justify your answer

Let y^2=4ax be a parallelogram and P be a point on it. Let the normal P intersects the x- axis at Q. Draw a line at Q perpendicular to the above normal. Show that this line intersects the parabola y^2+4a(x-2a)=0

The section of 2x^2+y^2=2(1-z^2) by the plane x+2=0 is a hyerbola.

True or false with full explanation

Find the equations of the spheres which pass through the circle x^2+y^2+z^2-6x+z+6=0, x-y=0 and touch the plane z=0

Find the new equation of straight line 2x+y=5 after rotating the axes through 45°.

Show that the co planar points A(2,3,2), B(4,7,6), C(1,2,3), D(-1,-2,-1) form a parallelogram

An engineer is working on making a diagram for the cooling tower he was going to to construct in the future. Cooling towers can be seen as towers with-inward curving sides, or simply, hyper-bola looking sides. His daughter ask him how high the center of the hyper-bolic sides of the tower was Y=+- 24/7x + 15, and he answers that the asymtotes of the hyperbola are the following:, and the area of its auxiliary rectangle os 168 square units. The daughter then finds the foci of the hyperbola. At what points on the cartesian plane are these foci found on?

How do I show that two given vectors are orthogonal