Subject Mathematics Medium ENGLISH
Faculty Renu Mam Status AVAILABLE
Category TOPIC BASED COURSE Lecture 77
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Point, Rectangular - Cartesian Coordinate system, Parametric and Polar Coordinates of a point, distance
between 2 points, section formula, Harmonic conjugate, Questions, About the Quadrilateral, Area of triangle,
Condition of collinearity of three points, Concurrent lines, condition of concurrency of three lines.

Area of quadrilateral, Area of n sided polygon.

Special points of triangle :
(1) Centroid (G) (2) Incentre (I) (3) Excentres (I1, I2, I3)
(4) Orthocentre (H) (5) Circum-centre(o)
Types of straight lines-
(1) General equation
(2) Slope - intercept form
(3) (a) Equation of a line parallel to x-axis.
(b) Equation of line perpendicular to x-axis.
(c) Equation of line coincident to x-axis.
(d) Equation of line coincident to y-axis.
(e) Equation of coordinates axes.
(4) Slope point form
(5) Two points form
(6) Determinant form
(7) Intercept form
(8) Normal or Perpendicular form.
Angle between two lines, condition of two lines to be parallel or perpendicular.

Condition of lines to be intersecting, Parallel, Coincident, Measurement of interior angle of Δ,
Questions based on point, special points and types of lines.

Questions based on special points and types of lines.

Equations of lines passing through P(x1, y1) and making an angle α with the line y = mx + C, slope of a line
equally inclined to the two given lines, Questions.
Parametric or distance form of a line.

Perpendicular distance, foot of perpendicular, foot of perpendicular, image of a point (x1, y1) w.r.t. line
ax + by + c = 0, distance between two parallel lines, Area of parallelogram, About the parallelogram, positions
of two points w.r.t. line/plotting of linear-inequations, condition that a point lies inside of a triangle.

Questions based on perpendicular distance, foot of perpendicular and image.

Locus, Steps how to evaluate locus of a point, questions, angle bisectors, types of angles bisectors, how to
identify type of angle bisector, angle bisectors containing a point P(x1, y1).

Questions based on angle-bisectors, family of lines (concurrent lines), Questions based on family of lines.

Pair of lines (combined or joint equations), Non-homogenous equation of second degree, homogeneous
equation of second degree, angle between pair of lines, separate equations from second degree, condition
that second degree non-homogenous equations represents pair of lines, point of intersection of pair of lines,
combined equations of angles bisectors of pair of lines.

Questions, distance between two parallel pairs of lines, Homogenisation.


Definition of Circle, Types of Circles-
(1) Centre - Radius form
(2) General equation : Equation of Circle passing through 3 non-collinear points.

Basic questions on circle, types of circles :
(3) Diameter form
(4) Standard equation of circle
(5) Parametric Form
(6) Point - Circle,
Intercepts formed by circle on coordinate axes, position of points w.r.t. circle, Some Important notes related
to Circle, Different-2 positions of circles, Questions.


Position of Line w.r.t. Circle, Length of chord Intercepted by the circle on, Tangent, Types of tangent-
(1) Slope - Form,
(2) Point - Form, Normal of Circle
(3) Parametric - Form
(4) Equation of tangent to the curve at (0, 0), number of tangents to the circle,
Questions, Application of tangents -
(1) Length of tangents
(2) Power of points P(x1, y1) w.r.t. circle
(3) Area of quadrilateral PACB
(4) Angle between two tangents
(5) Chord of contact
(6) Equation of chord whose mid point is given
(7) Director circle
(8) Separate equations of tangents
(9) Combined equations or pair of tangents
(10) Equation of circle circumscribing the ΔPAB
(11) PA.PB = PC. PD = PT2
(12) OA.OB = OC.OD
(13) Area of triangle formed by pair of tangents with their chord of contact, Questions


Questions, Position of 2 circles and their common tangents-
(1) When 2 circles are separated of each other, length of external and internal common tangent
(2) When two circles touches externally
(3) When two circles intersect at two real and distinct points, common chord of two circles, equation of
common chord and its length, maximum length of common chord, angle of intersection of 2 circles, orthogonal
circles and condition of orthogonality,
(4) When two circles touches internally
(5) When one circle lies completely inside of other, Questions.

Questions, Family of Circles-
(1) Equations of family of circles passing through the point of intersection of circles, s = 0 and line L = 0
(2) Equation of family of circles passes through 2 points A & B.
(3) Equation of family of circles passes through point of intersection of 2 circles.
(4) Equation of family of circles touching a curve at a point, Questions

Questions, Radical axis/Radical centre, Equation of circle cuts three given circles orthogonally, pole and


Introduction of Conic Section, Definition of Conic-Section, General equation of conic section, Locus of a
moving point P will be conic when focus(s) lies on directrix and does not lies on directrix,
Questions, some definitions related to conic -section
(1) Focus (2) Directrix (3) Axis (4) Vertex (5) Centre
(6) Focal- chord (7) Double- ordinate (8) Latus-Rectum (LR)
Standard parabola - Its all parameters, two questions.

Questions based on parameters of parabola, position of point w.r.t. parabola, Questions.

(1) Parametric equation of a chord
(2) Length of parametric chord
(3) Focal chord
(4) Minimum length of focal chord
(5) Focal distance
(6) 𝓁 (LR) = 2 (HM of 𝓁1 & 𝓁2), where 𝓁1 = PS, 𝓁2 = QS and P & Q are 2 moving points on parabola, S = focus,
(7) (a) If focal chord of parabola makes ∠angle with its axis then 𝓁(LR) = 4a cosec2 α.
(b) Length of focal chord at a distance p from vertex is  4a3÷p2
(8) If P1Q1 and P2Q2 are two focal chords of parabola y2 = 4ax then chords P1P2 & Q1Q2 intersect on its
(9) If P1P2 and Q1Q2 are two focal chord of parabola are at right angle then area of quadrilateral P1Q1 and P2Q2
is minimum when chords are inclined at an angle π/4 to the axis and its minimum area is 32a2.
(10) The circle described on any focal chord of parabola as diameter touches its directrix.
(11) A line having slope (m) passes through focus(s) cuts the parabola at two real & distinct points
if m ∈ R-{0}, Questions

Questions, Position of line w.r.t. Parabola, Condition of tangency
Types of tangent - (1) Point form (2) Parametric form
Questions based on tangents.

Questions based on tangents, common tangents of two curves,
Properties of tangents : P1, P2, P3, P4

Properties of tangents: P5, P6, P7, P8
Questions based on Properties of tangents, Normal, Types-
(1) Point form (2) Parametric form (3) Slope- form, condition of normality,
Questions based on normals, properties of normal, P1, P2, P3 (a, b, c, d), P4, P5 .

Properties of Normal- P6 , P7 (a, b), P8, P9- Reflection property,
P10, P11 (a, b, c)
P-11- Condition of three real & distinct normal to parabola, Questions based on normal and its properties,
(1) Number of tangents to a parabola,
(2) Pair of tangents
(3) Director - Circle
(4) Chord of contact
(5) Chord whose mid point is given, Questions

Introduction of ellipse and hyperbola, standard ellipse (when a > b and a < b) and standard hyperbola and
conjugate hyperbola, its basic parameters, auxiliary - Circle/Parametric coordinates of ellipse and hyperbola,
Alternate definition of ellipse and hyperbola, Some important notes, Questions determining the basic parameters
of ellipse and hyperbola.

Basic questions on ellipse and hyperbola, Questions based on Locus,
Questions based on Parametric coordinates.

Parametric equation of chord of ellipse and hyperbola, questions on parametric chord, position of line w.r.t.
ellipse Hyperbola, Condition of tangency, types of tangent-
(1) Slope form (2) Point form (3) Parametric Form,
Properties of tangents, Questions based on tangents.

Questions based on tangents and its properties, Pair of tangents, Equation of chord of contact, Equation of
chord whose mid point is given
#Director Circle, Questions, Normal of ellipse and Hyperbola, Types-
(1) Point Form (2) Parametric Form (3) Slope Form.

Questions based on normal of ellipse Hyperbola, Reflection Property of ellipse - Hyperbola,
Asymptotes of Hyperbola and conjugate Hyperbola, Properties of Asymptotes,

Rectangular (Equilateral) Hyperbola, Rectangular Hyperbola considered coordinate axes as its asymptotes,
its all parameters, tangents and normals, Questions.

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