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Verify if the point (2,4) lies on the curve x2 − xy − y2 + 4 = 0.

May 21, 2026Mathematics

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Verify if the point $(2,4)$ lies on the curve $x^2 - xy - y^2 + 4 = 0$ .
Substitute $x=2$ and $y=4$ into the equation:
$2^2 - (2)(4) - 4^2 + 4 = 4 - 8 - 16 + 4 = -16$
Since $-16 \neq 0$ , the point $(2,4)$ does not lie on the given curve. For a tangent line to exist at a point, the point must be on the curve.
Make an assumption to proceed.
We will assume there is a typo in the constant term of the curve's equation, and

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