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For the hyperbola x²/4 - y²/12 = 1, the tangent and normal are drawn at the upper end P(x1, y1) of the latus rectum (x1 > 0, y1 > 0). They meet the transverse axis at T and G respectively. Find the area of triangle PTG.

1. 45 sq units
2. 30 sq units
3. 90 sq units
4. 15 sq units

Correct answer: 45 sq units

Solution

With P = (4, 6), the tangent meets the x-axis at T = (1, 0) and the normal at G = (16, 0); base TG = 15 and height = 6 give area = 45 sq units.

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