The angle between a pair of tangents drawn from a point P to the circle x 2 + y 2 + 4x - 6y + 9 sin 2 + 13cos 2 = 0 is 2. Let any straight line PAB through the given point P(x 1, y 1) intersect teh circle S = 0 at two points A and B and if the tangents to teh circle at A and B meet at Q then locus of point Q is called the polar of the point P and the point P is called the pole of the polar with respect to given circle. You can get more clarity by viewing the video Result: Two angles at the circumference subtended by the same arc are equal. Result: Angles in the same segment are equal. Result: Angle between the tangent and the radius is 90°. The various results parallel to the above result are listed below: Then OA = OB = OP (radii), so we have two isosceles triangles OAP and OAQ. We shall prove the case 1 here and the rest cases follow on the same lines.Ĭase 1: Join PO and produce PO to Q. The proof can be carried on in three cases: Let AB be an arc of a circle with center O, and let P be any point on the opposite arc. A circle has centre (6, -5) and goes through the point (1, 7). At the more straightforward or superficial level, we have to know formulae, learn to recognise the. The circle which is centered at the origin with radius 1 is called the unit circle.Ī line segment whose end points lie on a circle is defined as a chord.Ī line that cuts a circle at two distinct points is called a secant.Ĭhords are equidistant from the center of a circle if and only if they are equal in length.Įqual chords of a circle subtend equal angles at the centerĪn arc is a section of the circumference of a circle.Ī sector is an area of a circle bounded by 2 radii.Ī segment of a circle is the part bounded by a chord and the circumference.Įqual arcs of a circle subtend equal angles at the center.Īn angle in a semi-circle is a right angle.Īn angle at the circumference of a circle is half the angle at the center subtended by the same arc. Questions on The Circle generally occur at two levels. Add to My Bitesize Remove from My Bitesize. The diameter is the longest chord of the circle. Circle theorems are used in geometric proofs and to calculate angles. Length of circumference in a circle is given by 2πr, where r is the radius. We first recall the important terms and formulae related to circles: Where t is a parameter ranging between 0 to 2π. In parametric form it may be represented as If the center is at (0, 0) then the equation becomes The general equation of a circle in Cartesian coordinates with centre at (a, b) and radius r is given by It can also be defined as the locus of a point equidistant from a fixed point. The distance between any of the points and the center is called the radius. The concepts of family of circles and that of common tangents to two circles under various configurations are given due importance.Ī circle can be defined as the curve traced out by a point that moves so that its distance from a given point is constant. In this chapter, we discuss the algebraic equations representing a circle and the lines associated with it i.e. a tangent, a pair of tangents and a chord of contact. The preliminary knowledge of the concept of Straight Lines is a prerequisite to study Circles. Concepts of Physics by HC Verma for JEEĬircle holds a high pedestal in the entire Syllabus of Co-ordinate Geometry in Mathematics. It is the easiest topic of coordinate geometry and with a bit of hard work, it becomes very easy to answer all the questions of this topic.IIT JEE Coaching For Foundation Classes.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |