Teaching Analytical Geometry

In the previous blog I mentioned about the assignment I got to teach Mathematics to PUC students. I started with teaching Analytical Geometry which many of the tuition teachers avoid telling it is difficult or little number of questions will appear from it for the exams. As per the syllabus of 2nd PUC conic sections includes parabola, ellipse and hyperbola. All the three conics have definite well defined properties so that they can be sketched or traced very well with a bit of practice. The books which are specifically written for 2nd PUC Mathematics doesn’t develop an analytical approach to deal with conic sections, but all are filled with tons of formulae which are very hard to remember.

Instead of making Analytical Geometry boring with lots of formulae, the equations of conics’ tangent, directrix, vertex and foci can be easily derived analytically just by developing skill of sketching curves. This requires a bit of patience to teachers and a bit of practice to students and an idea of co-ordinate axes. Once a student gets acquired with these skills it is just a piece of cake to write anything for a conic whether it is an equation for axis or a point such as vertex, foci or end points of latus rectum. Only thing which is necessary to teach analytical geometry is creating an interest towards sketching curves I feel rather than loading student’s brain with tons of formulae.

Conic sections have lot of applications in diverse fields ranging from a small manufacturing unit to the celestial bodies. Creating an interest towards conics is very much important and essential than making it just a part of syllabus essential to study to get through the examination!


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