Analytic Geometry Answers

Find the direction cosines of the perpendicular from the origin to the plane r.(6I+4j+2root3)+2=0

a circle has the equation x(to the power of 2)+y(to the power of 2)+12x+8y+7=0

a) write down the coordinates of the centre C

b) i) show that the line with equation x=13-2y is a tangent to the circle.

ii) find the coordinates of the point Q where the tangent and circle meet

c) the point P lies on the given line such that PQ=QC. Find the two possible coordinates of P

PN is any chord of the parabola y2 =4ax; the point M divides PN in the ratio m:n.find the locus of M.

show that the straight line x(p+2q)+y(p+3q)=p+q passes through a fixed point for different values of p and q

c) Find the angle between the x-axis and the tangent to the hyperbola xy = 9 at (3, 3).

Under what conditions on a, the sphere x^2+y^2+z^2+ax-y=0 and x^2+y^2+z^2+x+2z+1=0 intersect each other at an angle 45 degrees.

An elliptical riding path is to be built on a rectangular piece of property as shown below.
The rectangular piece of property measures 10 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.

how can i solve this please

Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by thirty six = 1



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Find an equation in standard form for the ellipse with the vertical major axis of length 18, and minor axis of length 16.

help me with this please