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Question
Find the equations of the tangents to the hyperbola `x^2/25 - y^2/9` = 1 making equal intercepts on the co-ordinate axes
Solution
Given equation of the hyperbola is `x^2/25 - y^2/9` = 1.
Comparing this equation with `x^2/"a"^2 - y^2/"b"^2` = 1, we get
a2 = 25 and b2 = 9
Since the tangents make equal intercepts on the co-ordinate axes, m = – 1.
Equations of tangents to the hyperbola
`x^2/"a"^2 - y^2/"b"^2` = 1 having slope m are
y = `"m"x ± sqrt("a"^2"m"^2 - "b"^2)`
∴ y = `-x ± sqrt(25(-1)^2 - 9)`
∴ y = `-x ± sqrt(16)`
∴ x + y = ± 4.
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