Math Notes

Analytic Geometry

Lines, circles, parabolas, ellipses, hyperbolas—equations, graphs, and solved examples.

Solved Problems

Circles

Plot the graph of the equation x^2 + y^2 +7x +5y-10=0.Find the equation of the circle with center at (1,7) and radius equal to 3.What is the graph of the equation \(18x^2 + 18 y^2 = 288\)What is the shortest distance between the curve \( x^2 -16x +y^2 +16y +64 =0 \) and the point (26,4)?

Theorems of Elementary Geometry

Prove that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.

Rectangular Coordinate System(Area of a Triangle)

Find the area of the triangle with the vertices given, (2,3), (1, 1)(-2,-2)

Ellipse

Write the equation of an ellipse where the distance between its directrices is 8, the distance between foci equal to 2, center at the origin, and major axis parallel to the x-axis.Write the equation of the ellipse having an eccentricity equal to 1/3, a distance between foci equal to 2, center at origin and major axis parallel to the x-axis.In the asteroid belt between the orbits of Mars and Jupiter some asteroids are known to have orbits with eccentricities as high as 2/3. For such an elliptic orbit, find the ration to major axis.

Parabola

Find the locus of the center of a circle which passes through (-2,3) and touches the line x=6.Find the equation of the parabola with axis parallel to 0x and passing through (5, 4) (11, -2),(21, -4,).

Curves. Functions

Find the point of intersection of the curve \(x^2 +y^2 = 25\) and \(3x + y =5\).

Straight Lines

Find the bisectors of the angles between the lines \(2x -y = 1\) and \(11x +2y = 5\).

Lines

Find the line perpendicular to \( \frac{x}{3} + \frac{y}{4} =1\)Equation of a Line

Tags:

analytic geometry conic sections circle equation parabola ellipse hyperbola coordinate geometry distance formula midpoint slope