PreCalculusConicSectionsProject.docx

PreCalculusConicSectionsProject.docx - Pre-Calculus Conic...

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Pre-Calculus: Conic Sections Project 1. A circle passes through P(5,9), Q(11,-3), and R(13,3). Find its equation in standard form, by doing the following steps: (a) Determine an equation of the perpendicular bisector of the segment PR. (b) Determine an equation of the perpendicular bisector of QR. (c) The perpendicular bisector of any chord of a circle will pass through the center. Thus, find the intersection of the two perpendicular bisectors above. This will be the center C of the circle. (d) To find the circle’s radius, find the distance of C from any of the three points P, Q, or R. you may use any of these three points. (e) What is the standard equation of the circle? 2. When expanded, the standard form of the equation of a circle can be written in the form x 2 +y 2 +Ax+By+C=0, which is the general form of its equation. (a)Substitute the coordinates of P(5,9) into its general form, yielding an equation in A, B, and C. Next, substitute the coordinates of Q(11,-3) and R(13,3),yielding two more equations. Solve these three equations for A, B. and C. (b) Using these values of A, B, and C, convert the equation to standard form. 3. Find the values of the constant k so that the graph of x2+y2-2kx+6ky=28-11k-9k2 is (a) a circle (b) a single point (c) the empty set 4. A one-way tunnel has the shape of a semi-ellipse that is 12ft high at the center and 28ft across. (a) Will a truck that is 8ft across and 10ft high be able to pass through the tunnel?
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