Instasolv

IIT-JEE NEET CBSE NCERT Q&A

4.5/5

# SL Loney Coordinate Geometry Solutions

SL Loney Coordinate Geometry Solutions by Instasolv have been prepared by using best techniques of solving questions based on all the elements of coordinate geometry related to polar and cartesian coordinates. SL Loney Solutions are written by the best team of Instasolv. S.L. Loney Elements of Coordinate Geometry Book is not only important from an exam point of view but also holds good in various fields of life.

S.L. Loney Solutions to the questions asked in Elements of Coordinate Geometry Book cover all the topics in totality. The major topics covered are algebraic results, coordinates, lengths of straight lines and areas of triangles, locus, rectangular coordinates for straight lines, polar equations and oblique coordinates, equations representing two or more straight lines, transformation of coordinates, the circle, systems of circles, conic sections, the parabola, the ellipse, the hyperbola, polar equation to a conic, tracing of curves, general equations and miscellaneous propositions.

SL Loney Elements of Coordinate Geometry solutions enable you to understand all the above topics in great depth and practise thoroughly. The solutions have been written very carefully to fulfil all your learning needs. You can refer to our solution for complete understanding and preparation of the concepts. This will certainly help you in securing good marks in Class 21 board and IIT-JEE exam.

S.L. Loney

## SL Loney Elements of Coordinate Geometry Solutions: Chapter-wise

S.L. Loney Coordinate Geometry Book consists of a total of 17 chapters. The topic-wise coverage of all the concepts in this book has been described below, along with the details of the questions asked.

## SL Loney Coordinate Geometry Chapter 1 (Introduction: Algebraic Results) Solutions

The first chapter of SL Loney Elements of Coordinate Geometry Solutions introduces you to the quadratic equations and roots of quadratic equations. It also tells you about determinant notation and determinants of second, third, fourth and higher orders. It also teaches you about elimination and its use in solving algebraic equations. The chapter contains 13 solved examples.

## SL Loney Coordinate Geometry Chapter 2 (Co-ordinates: Lengths of Straight Lines and Areas of Triangles) Solutions

Chapter 2 tells you about the coordinates, axes of coordinates, the origin of coordinates. Further, you come to know about the term abscissa, ordinate and quadrants. Next, you learn to find the distance between two points whose coordinates are given and points of coordinates which divide in a given ration (m1:m2) the line joining two given points (x1, y1) and (x2, y2). You also learn about polar coordinates for determination of the position of a point in a plane. This chapter has 81 questions in three exercises, all of the various difficulty levels.

## SL Loney Elements of Coordinate Geometry Chapter 3 (Locus: Equation to a Locus) Solutions

The 3rd chapter of SL Loney Coordinate Geometry Solutions teaches you that locus is a point which moves in such a manner so as to always satisfy a given condition or conditions where all the positions of the moving point must lie on the circumference of a circle. You come across various formulas related to this. Next, you learn about the equation to a curve. There are 23 questions in this chapter.

## SL Loney Coordinate Geometry Chapter 4 (The Straight Line: Rectangular Coordinates) Solutions

Chapter 4 teaches you how to find the equation to a straight line which is parallel to one of the coordinate axes. Further, you learn about a straight line through the points, angles between two given straight lines, conditions that they may be parallel and perpendicular, length of a perpendicular, and bisectors of angles between straight lines. Three exercises of this chapter of SL Loney Elements of Coordinate Geometry Book contain 95 questions of different types and levels of difficulty.

## SL Loney Coordinate Geometry Chapter 5 (The Straight Line: Polar Equations and Oblique Coordinates) Solutions

This chapter teaches you to find the general equation to a straight line in polar coordinates and polar equation of the straight line joining the points whose coordinates are (r1, θ1) and (r2, θ2). You also learn about equations involving an arbitrary constant and oblique coordinate, examples of loci, straight lines passing through fixed points. This chapter contains 68 questions in 3 exercises covering all the above concepts.

## SL Loney Coordinate Geometry Chapter 6 (On Equations Representing Two or More Straight Lines) Solutions

This chapter of SL Loney Elements of Coordinate Geometry Solutions teaches you all about angles between two lines given by one equation, homogeneous equation, equation to the straight lines bisecting the angle between the straight lines, and the general equation of the second degree and discriminant of the general equation. This chapter asks you to solve 70 questions of different types based on these topics.

## SL Loney Elements of Coordinate Geometry Chapter 7 (Transformations of Coordinates) Solutions

This chapter teaches you the situations where origin can be altered without the alteration of the direction of the axes and the situation where both can be altered to give transformation of coordinates. Here you come to know some more rules about the transformation of coordinates. This chapter has a total of 13 questions in 2 exercises.

## SL Loney Elements of Coordinate Geometry Chapter 8 (The Circle) Solutions

This chapter first introduces you to a circle, which is the locus of a point which moves so that its distance from a fixed point, called the centre, is equal to a given distance, which in turn is called the radius of the circle. In this chapter of SL Loney Elements of Coordinate Geometry Solutions you also learn about equation to a tangent, chord of contact, pole and polar, equation to a circle in polar coordinates, equation referred to oblique axes, and equations in terms of one variable. This chapter contains 133 questions.

## SL Loney Coordinate Geometry Chapter 9 (Systems of Circles) Solutions

This chapter teaches you about orthogonal circles and its properties, radical axis of two circles and geometrical construction for the radical axis of two circles, radical centre, coaxial circles and how to find the equation of a system of coaxial circles. This chapter contains 31 questions through 2 exercises.

## SL Loney Coordinate Geometry Chapter 10  (Conic Sections: The Parabola) Solutions

This chapter of SL Loney Coordinate Geometry Solutions teaches you all about conic sections and the terms focus, eccentricity, directrix, axis, parabola, the vertex of parabola, ellipse and hyperbola. You learn to find the equation to a parabola, equation to a tangent, some properties of the parabola, pole and polar, diameters, and equations in terms of one variable. You also learn to express coordinates of any point on the parabola in terms of one variable.  This chapter has 4 exercises with 90 questions.

## SL Loney Elements of Coordinate Geometry Chapter 11 (The Parabola) Solutions

The 11th chapter of SL Loney Elements of Coordinate Geometry Book is a continuation of chapter 10 and gives more information about parabola. You learn about loci connected with the parabola, three normal passing through a given point, and parabola referred to two tangents as axes. This chapter contains 69 questions in 3 exercises.

## SL Loney Coordinate Geometry Chapter 12 (The Ellipse) Solutions

This chapter tells you that the ellipse is a conic section in which the eccentricity e is less than unity. You learn more about properties of the auxiliary circle and eccentric angle, equation to a tangent, some properties of the ellipse, pole and polar, diameter, conjugate diameters, supplemental chords, four normal through any point and examples of loci. There are 115 questions in 4 exercises of this chapter.

## SL Loney Elements of Coordinate Geometry Chapter 13 (The Hyperbola)

This chapter tells you that hyperbola is a conic section in which the eccentricity e is greater than unity. Further, it teaches you about latus-rectum of the hyperbola, central conics, director circle, asymptotes, equilateral or rectangular hyperbola, conjugate hyperbola, equation referred to the asymptotes as axes, one variable. You can find 84 questions of different difficulty levels in 3 exercises of this chapter of SL Loney Elements of Coordinate Geometry Solutions.

## SL Loney Coordinate Geometry Chapter 14 (Polar Equation of a Conic Section, Its Focus Being the Pole)

This chapter teaches you all about, polar equation to a tangent, equations to the directrices, equations to the asymptotes and properties of polar and normal equations of tangents. This chapter has 27 questions for your practice.

## SL Loney Coordinate Geometry Chapter 15 (General Equations of the second Degree: Tracing of Curves) Solutions

The chapter number 15 of SL Loney Coordinate Geometry Book deals with particular cases of conic sections including an ellipse, a parabola, a hyperbola, two straight lines (real, imaginary, intersecting, coincident, or parallel), transformations of the equation to the center as origin, equation to asymptotes, tracing a parabola, tracing a central conic, and eccentricity and foci of general conic. This chapter contains two exercises and 71 questions in them.

## SL Loney Elements of Coordinate Geometry Chapter 16 (The General Conic) Solutions

This chapter tells you all about tangent, conjugate diameters, conics through the intersections of two conics, the equation S = λuv, general equation to the pair of tangents drawn from any point, the director circle, the foci, the axes, lengths of straight lines drawn in given directions to meet the conic, conic passing through four points, conics touching four lines, and that the conic LM = R2. This chapter consists of 70 questions in 4 exercises.

## SL Loney Coordinate Geometry Chapter 17 (Miscellaneous Propositions)

The 17th chapter of SL Loney Elements of Coordinate Geometry Book deals with the miscellaneous problems on conic. You learn about the four normals from any point to a central conic, confocal conics, circles of curvature, the evolute of a curve and contact of the third order and envelopes. This chapter consists of 78 questions in 4 exercises.