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Tangents are drawn to the hyperbola x²/9 - y²/4 = 1 parallel to the straight line 2x - y = 1. Find the points of contact of these tangents on the hyperbola.

1. (9/(2*sqrt(2)), 1/sqrt(2)) and (-9/(2*sqrt(2)), -1/sqrt(2))
2. (3*sqrt(3), -2*sqrt(2)) and (-3*sqrt(3), 2*sqrt(2))
3. (9/(2*sqrt(2)), -1/sqrt(2)) and (-9/(2*sqrt(2)), 1/sqrt(2))
4. (3, 2) and (-3, -2)

Correct answer: (9/(2*sqrt(2)), 1/sqrt(2)) and (-9/(2*sqrt(2)), -1/sqrt(2))

Solution

Setting the tangent slope to 2 gives x1 = (9/2) y1; substituting into the hyperbola yields y1 = +/-1/sqrt(2) and x1 = +/-9/(2 sqrt(2)).

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