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An equation of a tangent to the hyperbola 16x 2 -25y 2 -96x+100y-356=0 which makes an angle of π/4 (45*) with the transverse axis is ?

An equation of a tangent to the hyperbola 16x2-25y2-96x+100y-356=0 which makes an angle of π/4 (45*) with the transverse axis is ?

Grade:12th Pass

1 Answers

Arun
25750 Points
5 years ago
Dear Vasu
 
16(x² - 6x +9) - 25(y² -4y +4) = 356 +144 -100 = 400
(x-3)²/25  - (y-2)² /16 = 1
Now tangent to parabola
y-2 = m(x-3) ± sqrt (a²m²-b²)
All the things are known except m.
But m = 1 
Hence
y-2 = (x-3) ± sqrt( 25-16)
y-2 = (x-3) ± 3
Hence
y = x +2 
&
y = x -4

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