Analytic Geometry Answers

x^2-9y^2+36y-45=0

the axial cross section of a head light reflector is a parabola with the bulbs center as focus. find the depth of the headlight in centimeters, if the bulbs center is 2 centimeter. from the vertex and the radius of the head light is 10 centimeter

intercepts made by the line of shortest distance.

In the following problem,
The line of shortest distance of the lines (x/2)=(-y/3)=(z) and (x-2)/3=(y-1)/-5=(z+2)/2
intersects these two lines in P andQ respectively.
1.find the coordinates of P
2.find the coordinates of Q.
i can find the shortest distance between these two lines.but how to find the points of intersection with the line of shortest distance?

The line L is tangent to a circle, center at (2.5), at point (-1,1). Suppose line L is passing through (-5,4). Determine the equation of the line L.

What is an equation of the line that passes through the point (-3,-11) and is parallel to the line whose equation is 2x-y=4?

two complementary angles are in the ratio 1:8 find the measures of both angles

salam sir please help me by providing the answer of below question.
how many triangles can be formed by joining 12 points ,7 of which lies on the same straight line.

three consecutive vertices of a parallelogram (1,-3),(-3,-1), (3,5). FIND THE 4TH VERTEX?

Determine in two ways whether or not the points A (-1,-1), B(4,1) and C(12, 4) lie on a straight line. Is AB + BC = AC? Is area ABC zero ?

Find the points which trisect the segment joining the points (-3,5) and (9,2).