## Ashish Bajpai is teaching live on Unacademy Plus

Hyperbola Definitions ->S tandord Equati on Relatiam between focaL distances Relative position of a poind with resped the Hyper bola Poraetric Coordimates

Intersectiom of a Jine and a Hyper bala Let the inemx+Cint erset the yprbola oc liminating y beteen the wo 2 equat ions e get mox+C) 2 CI)

Ldx, sc2_ be the roots f this 9uaan atic in We find thaA, in gene Yak a Jine inters ects the hyperbola a twa points The discriminant a c (JO 2 II the oots arc real and equal then

mxt/s ect the hyper bala a one point f.e Houch the hype bala In this asehe Yoots of (1) ane

and hence TA impres tlak the lines y = mx-C Guc h the hyperbola at 2 a Tm

A Lime through the poin contack POY Q and Perpendicular to the tangcrt atP oa Called a norma the hyperbola Equation of the chord be to Doi nts on the hyperbola We have

Hence the quation of the chard PS is

RCh.k) is the mid-point of PO tlem h,"122 K- 3+y and the Slope ofthe chord Pa 2 md the equation f the chard Pa i th h mid- point R is 2. bh (x-h) 2 4 1) 2 2

the the Chord Pa becomes tamg ent to she 7) P (X12%) equation (1) beco m es 9 1 C3)

Cs) is the equation of the tong end d PCX, '%) to the hyper bola 2 The Slope of the ang end is bLx; Hence 61 x

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