Circles and Conic Sections
A torch beam, a satellite dish, the path of a thrown ball, the orbit of a planet and the arch of a bridge all follow one family of curves.
- You slice a cone with a flat plane and you get a circle, an ellipse, a parabola or a hyperbola.
- This chapter studies them with coordinates.
- You write the equation of a circle and of the tangent to it, work with pairs of circles, and then meet the parabola, the ellipse and the hyperbola through their focus and directrix.
- It covers the unit of the Indian syllabus (NCERT, JEE Main, BITSAT, WBJEE, the state entrance exams) and the matching topics of A-Level Pure and Further Maths.
- Python checks every point, line and curve on the computer.
Part of Mathematics · High School (11–12) (chapter 21)
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Courses in This Path (4)
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The Circle: Equations, Lines and Tangents
Where is the centre of a round pond when you know three points on its shore? Start from the distance of a point from a fixed centre and write the equation of a circle in its standard and general forms. Then place a point and a line against a circle, find the length of a chord, and draw the tangent and the normal. You end with the tangents from a point outside, the length of a tangent and the chord of contact. It covers the first part of the Indian syllabus unit (NCERT, JEE Main) and the matching topic of A-Level Pure Maths.
Systems of Circles: Radical Axis, Common Tangents and Families
Two round ponds overlap, and a fence is to run along the line through the two meeting points. Where does that line lie? Look at two circles together: how they touch, cut or miss, how many common tangents they have, and what their radical axis is. Then meet orthogonal circles, the circles through the meeting points of two curves, and the locus questions that the entrance exams love. It covers the second part of the Indian syllabus unit (NCERT, JEE Main) and goes beyond the circle work of A-Level Pure Maths.