Analytic Geometry

Three vertices of a rectangle are (2,5), (-3,5) and (2,-1). Find the coordinates of the fourth vertex.

Find the area of a triangle formed by the intersection of three lines, x + y – 6 = 0, 2x – 4y = 0, x – y – 4 = 0.

Find the area of a pentagon connecting the points (3,0), (2,3), (-1,2), (-2,-1) and (0,-3).

Find the inclination of the line that passes through the points (4, -3) and (-1, 3).

Find the acute angle formed by the lines 2x + y – 8 = 0 and x + 3y + 4 = 0.

The midpoint of the line segment between P₁(x,y) and P₂(-2,4) is Pm(2, -1). Find the coordinates of P₁.

Find the distance between the point A(3,4) and the line 5x + 12y – 10 = 0.

Find the distance between the lines 4x – 3y = 12 and 8x – 6y = -16.

A circle whose equation is x² + y² + 4x + 6y – 23 = 0 has a center at:

A circle whose equation is x² + y² – 6x – 4y -12 = 0 has a diameter of

What is the distance between the center of the circles x² + y² + 2x + 4y – 3 = 0 and x² + y² – 8x – 6y + 7 = 0?

Find the radical axis of the circle x² + y² + 8x – 6y = 0 and the circle x² + y² -12x -16y + 20 = 0.

The ratio of the distance between the foci to the distance between the vertices in either hyperbola or ellipse.

Find the equation of the directrix of the parabola (y-2)² = -8(x-1).

A parabola has its focus at (7,-4) and directrix Y = 2. Find the equation.

Find the axis of symmetry of the function y = 2x² – 7x + 5.

An arch 18 m high has a form of parabola with a vertical axis. The length of the horizontal beam placed across the arch 8 m from the top is 64 m. Find the width of the bottom.

Find the length of the latus rectum of the parabola whose equation is y² = 20(x+6).

The equation 25X² + 16Y² – 150X + 128Y + 81 = 0 has its center at

The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth.

The arch of an underpass is a semi – ellipse 60 ft wide and 20 ft high. Find the clearance at the edge of a lane if the edge is 20 ft from the middle.

Find the coordinates of the center of the curve whose equation is 16x² – 25y² + 160x – 200y + 400 = 0.

Find the length of the latus rectum of the hyperbola whose equation is 4x² – 9y² + 8x – 54y -113 = 0.

The semi-transverse axis of the hyperbola whose equation (x – 5)²/9 – (y – 6)²/4 = 1 is

Find the polar equation of a circle with center at the (3,0) and the radius 3.