Find the equation of the tangent to the hyperbola x2 ndash 4y2 36 which is perpendicular to the line...........

Mathematics (NDA) Coordinate Geometry

Find the equation of the tangent to the hyperbola x² – 4y² = 36 which is perpendicular to the line x – y + 4 = 0?

y-x =±√27

y+x =±√26

- y+x =±√27

y+x =±√27

Let m be the slope of the tangent , tangent is perpendicular to the line x – y = 0

x – y = 0

y=x

m1=1

m×m1=-1

m.1=-1

m=-1

Since x² – 4y² = 36

x²/36 -y²/9 =1

a²=36 ,b²=9

equation of tangent are y=(-1)x± √36(-1)²-9

y=-x± √27

y+x =±√27

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