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Two curves C1: x² - y² = 8 and C2: 9x² + 25y² = 225 intersect at the point P = (-5/sqrt(2), 3/sqrt(2)). Find the angle of intersection of the normals to C1 and C2 at point P.

1. 0
2. pi/4
3. pi/3
4. pi/2

Correct answer: pi/2

Solution

The tangent slope to C1 at P is m1 = x/y = -5/3, and to C2 is m2 = -9x/(25y) = 3/5. Since m1*m2 = (-5/3)*(3/5) = -1, the tangents are perpendicular, so the normals are also perpendicular and the angle between them is pi/2.

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