Analytic Geometry Answers

suppose the point P=(1,2) lies on line L. Suppose that the angle between the line and the vector N = <3,4> is 90° (whenever this happens wa say vector N is normal to the line). Let Q = (x,y) be another point on the line L. Use the fact that N is orthogonal to PQ to obtain an equation of the line L.

What is the gradient of a line that has an angle of inclination of 50°?

Enter your answer, rounded to 4 significant figures,

Find the direction cosines of the perpendicular from the origin to the plane r.(6I+4j+2root3k)+2=0

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 3 cos 5θ

Find an equation in standard form for the hyperbola with vertices at

(0, ±6) and asymptotes at y = ± 3 divided by 5xx

Find the vertices and foci of the hyperbola with equation.

quantity x minus 3 squared divided by 81 minus the quantity of y plus 5 squared divided by 144 equals 1

Find the center, vertices, and foci of the ellipse with equation 2x2 + 7y2 = 14

Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.

How conic sections are generated. From your surrounding give four examples of each of circle, parabola, ellipse and hyperbola. Prepare a list of their different informations.

Base of an equilateral triangle lies along the line 9x+40y-50 and its vertex opposite to the base lies
on the line 9x+40y+32=0. Find the length of the side of the triangle and also find its area.