The normal to the curve, x2 + 2xy

Engineering

Mathematics

Tangent and Normal

Question

The normal to the curve, x² + 2xy – 3y² = 0, at (1, 1)

meets the curve again in the fourth quadrant.

meets the curve again in the third quadrant.

does not meet the curve again.

meets the curve again in the second quadrant.

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Slope of normal at (1, 1) on the curve = – 1

$∴$ Equation of normal is x + y = 2 ......(A)

Put y = (2 – x) in the curve x² + 2xy – 3y² = 0, we get (1, 1) and (3, – 1)