An equation of a tangent to the hyperbola 16x^2 -25y^2 - 96x + 100y - 356 =0 which makes an - Maths - Conic Sections

Question

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

Lovina Kansal · Accepted Answer

Dear student
Equation of the hyperbola can be written aX252-Y242=1    
(1)where X=x-3 and Y=y-2Equation of tangent which makes an angle π4, with the transverse axis X=0 of (1) isY=tanπ4X±25tan2π4-16⇒y-2=x-3±25-16⇒y-2=x-3±3⇒y=x+2 or y=x-4
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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 ?/4 with the transverse axis is ???