Math, asked by Rajdeep7424, 1 month ago

no. of tangent to the hyperbola x²/a²-y²/b²=1 is parallel to x axis are​

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Answered by Mrlenged
71

Solution:-

Equation of line through (b,a) is

y−a=m(x−b)</p><p></p><p>y=mx+(a−mb)</p><p>Condition  for  line  y=mx+c  to  be  a  tangent  to  hyperbola  is c2=a2m2−b2</p><p>⇒(a−mb)2=a2m2−b2</p><p>⇒a2+m2b2−2amb=a2m2−b2</p><p></p><p>m2(b2−a2)−2abm+a2+b2=0</p><p>⇒m1m2=tanθ1tanθ2=b2−a2a2+b2=2</p><p>⇒b2−a2=2a2+b2</p><p></p><p></p><p>

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