CIRCLES (L-1)|INTRODUCTION,CENTRE-RADIUS,TYPES OF CIRCLES|RENU MAM|JEE MAIN-ADV.|TAYAL CLASSES MATHS

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Tayal Classes is an e-learning service specifically for JEE Maths to help the JEE aspirants prepare for JEE Mains & Advanced. In this session, Renu Ma'am will be discussing JEE Maths chapter 'CIRCLE ' and tips and tricks to solve questions to let you be thorough according to JEE Mains & JEE Advanced. Watch this video to know the best strategy to solve questions from 'CIRCLE '. All Subject Matter Experts at Tayal Classes have been always ready to give the best guidance for JEE Maths for JEE preparation by analyzing the important needs of the students and give them a straight pathway to get through IIT JEE.
We have multiple available Mathematics IIT JEE courses at Tayal Classes -

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2. 2020 - Integrated JEE (XI + XII)
3. 2020 - XII JEE + XII NCERT & Previous Five Years Papers (with Solutions)
4. 2020 - XII NCERT & Previous Five Years Papers (with Solutions)
5. 2020 - XI JEE (Main + Advanced)
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THIS CHAPTER CONTAINS FOLLOWING SUBTOPICS LECTURE-WISE

01) (51.50 Min.) Introduction of circle, about its centre and radius. Types of circles -
(1) Centre, (2) Conversion of general equation of circle into centre radius form, Evaluating its centre and radius. Method 1 – Taking general equation of circle and by putting 3 points, make 3 equations in 3 unknowns. Method 2 – Find circumcentre and circumradius of a triangle passing through these 3 points. Method 3 – Write equations of family of circles passing through any two points and satisfy third point in it. Example explaining it.
Equation of circle passes through origin.
Basic questions based on evaluating centre and radius of circle and types of circles. Questions – ( 1- 6)
02) (47.43 Min.) Types of Circle
(3) Diameter form (4) Standard equation of circle
(5) Parametric Form – in standard equation or in general equation of circle. Example
(6) Point of circle. Intercepts formed by circle on coordinate axes – x intercept, y-intercept
Some –important notes –
(1) Condition for 2 circles touches externally and internally.
(2) Image of a circle wrt. Line
(3) Maximum length of chord.
(4) Intersection of two circles and their common chord and maximum length of
common chord.
(5) Equation of circle circumscribing a quadrilateral when equations of its side are
given.
Different-2 positions of two circles-
(1) When circle touches the x-axis.
(2) When circle touches the y-axis
(3) When circle touches both the coordinate axes.
(4) When circle passes through (0,0) and cuts the intercepts a and b on positive
coordinate.
(5) When circle touches the x-axis and cuts intercept ‘’ and y-axis.
03) (46.57 Min.) Questions based on type of circle, intercept of circle on coordinate axes nearest and farthest point on the circle from given point-
Questions – (1-4, 5-(i), (ii), 6, 7)
04) (32.09 Min.) Some more advanced level questions -
05) (60.41 Min.) Position of line wrt circle -
Length of chord intercepted by the circle on the chord.
Tangent – Types of tangent (1) Slope Form (2) Point Form
Equation of tangent of general equation of circle at point (x1, y1)
Equation of tangent of 2nd degree non-homogeneous curve at point (x1, y1)
Examples.
(3) Parametric Form
(4) Tangent to the curve at origin (0,0) axes.
Number of tangents to the circle according as position of point w.r.t. circle.
Questions – (1, 2, 3-a, b, 4, 5, 6)
06) (45.55 Min.) Application of tangents -
07) (44.31 Min.) Questions based on applications of tangents – ( 1- 6)
Some more advanced level questions on application of tangents – (1 – 10)
08) (44.49 Min.) Questions based on application of tangents – (11 – 17)
09) (36.58 Min.) Advanced level questions on application of tangents.
10) (46.09 Min.) Position of two circles wrt each others -
11) (59.21 Min.) Questions based on position of two circles wrt. Each other and its common tangents – (1-a, b, c, d, 2, 3, 4). Questions – (1 – 16)
12) (46.46 Min.) Family of Circles –
13) (41.06 Min.) Questions – (6, 7, 8)

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