Question

a) Show that the points P (3, -1), P (6, 3), and P (-2, 9) are not on the same line. b) Show that a right triangle has corners. Write the perpendicular lines passing through the perpendicular corners of the triangle. 2. x + 3xy + 2y? Indicate the type of conic given by the equation 3x + 4y + 2 = 0 and show that it is degenerate. Find out which equation the distorted cone indicates and draw it. 3. Determine the type of conic given by the equation 5x + 8xy + 5y - 25 = 0, find the reduced equation, and draw it. 4. Determine the type of conic given by the equation 9x - 16y + 18x - 64y + 55 = 0, show whether it is broken or not. Find the reduced equation of the conic and draw it. 5. The equation x + Bry + 4x - 4y + 8 = 0 is defined as the set (geometric location) of points whose distances are equal to the point F (-2, 2) and to the y = 0 line. According to this definition, find the constant B, write the type of the equation, find its focus and directrix equation, and draw it.

          a) Show that the points P (3, -1), P (6, 3), and P (-2, 9) are not on the same line.
b) Show that a right triangle has corners. Write the perpendicular lines passing through the perpendicular corners of the triangle.

2. x + 3xy + 2y? Indicate the type of conic given by the equation 3x + 4y + 2 = 0 and show that it is degenerate. Find out which equation the distorted cone indicates and draw it.

3. Determine the type of conic given by the equation 5x + 8xy + 5y - 25 = 0, find the reduced equation, and draw it.

4. Determine the type of conic given by the equation 9x - 16y + 18x - 64y + 55 = 0, show whether it is broken or not. Find the reduced equation of the conic and draw it.

5. The equation x + Bry + 4x - 4y + 8 = 0 is defined as the set (geometric location) of points whose distances are equal to the point F (-2, 2) and to the y = 0 line. According to this definition, find the constant B, write the type of the equation, find its focus and directrix equation, and draw it.

Added by Terri L.

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