Math Assignment Help With Intersection Of A Line And Hyperbola

7.6.6 Intersection of a line and Hyperbola:

The only condition for a line y = mx + c to be tangent on hyperbola x² + y² is;

a² b²

c = ± √a²m² – b²

Example: Find the point of contact of a line 5x + 2y = 9 touching the hyperbola x² – 9y² = 9.

Solution: The given line is 5x + 12y = 9 ….(i)

The given hyperbola is x² – 9y² = 9. ….(ii)

9x² – 90x +225 = 0

X² – 10 x + 25 = 0

(x – 5)² = 0

X = 5, 5 are the two coincident roots.

Putting x = 5 in (i) we get y = -(4/3)

Therefore,

The point of contact is (5, -4/3)

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