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Properties of Hyperbola

  Hyperbola: 75525.png
Definition of curve w.r.t. triangle If the base of triangle is given and opposite vertex moves in such a way that difference of two variable side is constant then locus of moving vertex is hyperbola
 
Position of a point P(hk) with respect to curve
 
75519.png

P will lie outside, on or inside the hyperbola 75513.png = 1 according as 75507.png – 1 <, =, > 0
 
Equation of tangent to curve at point P(x1y1) 75501.png or T = 0
Equation of tangent to curve at point whose eccentric angle is φ 75495.png tan φ = 1
Equation of tangent to curve whose slope is m y = mx ± 75489.png
Equation of normal to curve at point P(x1y1) 75482.png
Equation of normal to curve at point whose eccentric angle is φ 75475.png
Points of contact when y = mx + ctouches the curve 75468.png
Equation of chord contact w.r.t. any point P(x1y1) 75462.png
Equation of chord PQ which bisected at point R(x1y1) 75456.png
Pair of tangents from point P(x1,y1) 75449.png or T2 = SS1
Locus of point of intersection of tangents which are perpendicular or equation of director circle x2 + y2 = a2 – b2 (a > b)
Equation of the chord joining the points P(φ1) and Q(φ2) 75443.png75437.png




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