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Question

The slope of the tangent to the hyperbola x225y216=1 which passes through the point (1,4) is

A
1
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B
43
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C
2
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D
1
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Solution

The correct options are
A 1
B 43
The equation of a tangent is y=mx±a2m2b2
Hence, y=mx±25m216 is the equation of a tangent to the hyperbola.
This passes through (1,4), so 4=m±25m216
168m+m2=25m216
24m2+8m32=0
m=1,43

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