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Question:

The tangent and normal to the ellipse 3x² + 5y² = 32 at the point P(2, 2) meet the x-axis at Q and R respectively. Then the area (in sq. units) of the triangle PQR is

143

163

3415

6815

Solution:

Correct option is C. 68/15
3x² + 5y² = 32
|dy/dx|(2, 2) = -3/5
Tangent: y - 2 = -3/5(x - 2) ⇒ Q(16/3, 0)
Normal: y - 2 = 5/3(x - 2) ⇒ R(4/5, 0)
Area is = 1/2(QR) × 2 = QR = 68/15