Question

the equation of the tangent at the point (2,4) to the hyperbola xy=8 is​

Answer 1

Answer:

Consider a hyperbolaand a line. O is the centre of hyperbola. Tangent at any point P of hyperbola intersect the coordinate axes at A and B. <br> Let the given line intersects the x-axis at R. if a line through R. intersect the hyperbolas at S and T, then minimum value of is

2

4

6

8

Answer :

D

Solution :

Letbe a point on the hyperbola. Equation of the tangent at this point. <br><br> Locus of circumcentre of triangle is<br> Its eccentricity is<br> Shortest distance exist along the common normal. <br>or<br>Foot of the perpendicular is<br>Shortest distance is distance of C from the given line which is<br> Given line intersect the x-axis atAny point on this line at distance 'r' from R isIf this point lies on hyperbola, then we have<br> Product of roots of above quadratie in 'r' is, which has minimum value 8 <br>Minimum value ofis 8