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A tangent to the ellipse x²/18 + y²/32 = 1 has slope -4/3. It cuts the x-axis at A and the y-axis at B. With O the origin, find the area of triangle OAB.
- 12 sq. units
- 36 sq. units
- 24 sq. units
- 30 sq. units
Correct answer: 24 sq. units
Solution
Here a² = 18, b² = 32, m = -4/3, so c = sqrt(18*16/9 + 32) = sqrt(32+32) = 8; the intercepts give area = (1/2)*(c²/|m|) = (1/2)*(64/(4/3)) = 24.
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