Acute Angle Definition Acute Angle Definition Acute angle is one of the types of angles whose measure is below 90 degree and above 0 degree. The general form of an acute angle is 0 < theta < 90. Some examples of acute angles are 45 degree, 75 degree and 60 degrees. The study of angles comes under the branch of Geometry. Students can get more solved examples, diagrams, explanations and other related material that are useful for their homework in the Geometry homework help page. What is an Acute Angle ? Acute angle is an angle that lies between o degrees and 90 degree. The acute angle picture is as follows Here JKL is an acute angle. Its measurement is equal to â&#x2C6; JKL = 75 degree. It can also be represented as â&#x2C6; K = 75 degree. Here, K is the edge point of an angle. It is also called as the vertex of an angle and then the rays JK and KL are the arms of the angle. The angle values gets changed based on the rays. Know More About Simultaneous Equation Solver
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Finding Acute Angles Identify whether the angles given below are acute angles or not:
Students can get help in understanding the concepts better and in solving problems involving acute angles on the Geometry help page.
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Hyperbola Formula Hyperbola Formula Unlike some geometric figures, which have one definition, hyperbola has more than one definition. A hyperbola can be defined as a plane curve having two branches, formed by the intersection of a plane with both halves of a right circular cone at an angle parallel to the axis(major and minor) of the cone. It is thelocus ofpoints satisfying the condition that the difference of distances fro m two points foci is always constant. This is the hyperbola definition in geometry. The equation of hyperbola is given by x2/a2 - y2/b2 = 1 where origin is the centre. Hyperbola as a locus of points: So a hyperbola is a locus of points P in a plane such that PF = distance from focus = e.PD where PD is the perpendicular distance of P from directrix D. There will be two directrices parallel to minor or conjugage axis, two foci equidistant from centre. For a hyperbola, eccentricity = e > 1. The two crossing lines passing through centre of the hyperbola are called asymptotes and they never meet the curve at finite points. The hyperbola looks bounded by the asymptotes and open curve. More about hyperbola: The only difference between the equation of ellipse and hyperbola is sign of second term. Math.Tutorvista.com
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That means in ellipse b is real, and in hyperbola b is imaginary. The parametric equation of hyperbola is expressed in terms of hyperbolic functions as x = acosh μ and y = b sinh μ. where μ is the angle of the asymptotes with the line of foci (transverse axis) Terminologies of Hyperbola Foci: The foci coordinates are given by (ae, 0) and (-ae, 0) for a hyperbola with centre (0,0). Foci are points inside the hyperbola, when centre is not origin.When centre of hyperbola is (h,k) say then equation of the hyperbola with a,b as semi major and minor axis is (x-h)2/a2 -(yh)2/b2 =1. For these hyperbolas, foci is given as (h-ae,k) and (h+ae,k) Formula for eccentricity: In an hyperbola, a, b and e are related by the equation a2(e2-1) = b2 or e = root of (1+ b2 / a2) In a hyperbola, eccentricity >1 always. Directrices: Directrices are two lines parallel to conjugate axis and satisfy the distance definition found in the hyperbola. Directrices always lie outside the hyperbola. Asymptotes: Asymptotes are lines passing through centre, and have slopes as -b/a and b/a. They never cut the hyperbolic curve at finite points. Middle rectangle: The hyperbolas normally remain outside the middle rectangle with length between two vertices (2a) and width equal to 2b with b on either side. In other words, the rectangular area is always not inside the hyperbolic curve
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