CIRCLES | QUICK REVISION | JEE Main | JEE Advanced | BITSAT – By Nitesh Choudhary - Videos

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In this video, we will revise the topic CIRCLES.
I will start the topic by discussing the equation of circle in different forms. We will discuss – Finding centre and radius of circle if the equation is given, Equation of circle with centre and radius given, Equation of circle whose end points of diameter is given, Equation of Circle with coordinate axes, Length of x-intercept made by a circle, Length of y-intercept made by a circle, Equation of circle passing through two given points having least area / radius / perimeter.
Next, we will discuss topics related to a point and a circle. What are the conditions that needs to be applied if the point lies inside the circle, on the circle or outside the circle. We will also discuss how to find the maximum or minimum distance of a point from a circle.
Next discussion will be related to equation of tangent to a circle. First topic is, what is the condition to be applied given a line is tangent to a circle or line is chord to a circle – slope form of tangent. How to find the equation of a tangent, point of contact on circle is given i.e. point form of tangent. How to find the locus of point of intersection of two perpendicular tangents i.e. Director Circle. What is the formula to find the length of tangent from an external point to the circle. How to find the angle between tangents drawn from the external point. How to find the equation of the circle circumscribing the triangle formed by pair of tangents and the chord of contact. How to find the area of the triangle formed by pair of tangents and the chord of contact. How to find the length and equation of the chord of contact to a circle. Formula to find the equation of pair of tangents to the circle. How to find the equation of chord with middle point given and equation of normal to the circle.
Next, we will discuss different cases related to two circle. What are the conditions that needs to be applied given two circles; neither touches nor intersect each other, touches each other externally, intersect each other, touches each other internally, one circle is inside the other. We will also discuss number of common tangents in each cases. How to find the length of external or direct common tangent and the length of internal or transverse common tangent.
Next is equation of common chord and common tangent to two given circles. We will also discuss the condition such that two given circle intersect each other orthogonally i.e. tangents at their point of intersection include a right angle. At last, we will discuss different cases of family of circles – Circle Through Point Of Intersection Of Two Given Circles, Circle Through Point Of Intersection Of A Circle & A Line, Circle Through 2 Given Points A (x_1,y_1) and B(x_2,y_2), Circle Touches A Fixed Line L=0 At The Point (x_1,y_1).

By – Nitesh Choudhary
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