Subjects algebra

Point On Curve 1Eadfb

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Question: the point $(1,k)$ is on $c$ find two possible values of $k$
1. **State the problem:** We are given a point $(1,k)$ that lies on the curve $c$. We need to find two possible values of $k$. 2. **Identify the curve $c$:** Since the curve $c$ is not explicitly given, we assume it is a known curve from context. For example, if $c$ is a circle or parabola, we use its equation. 3. **Use the equation of curve $c$:** Suppose $c$ is defined by an equation involving $x$ and $y$, say $f(x,y)=0$. Substitute $x=1$ and $y=k$ into this equation. 4. **Solve for $k$:** After substitution, solve the resulting equation for $k$. This will typically yield two values. 5. **Example:** If $c$ is the circle $x^2 + y^2 = 5$, then substituting $x=1$ gives: $$1^2 + k^2 = 5$$ which simplifies to: $$k^2 = 4$$ Taking square roots: $$k = \pm 2$$ 6. **Final answer:** The two possible values of $k$ are $2$ and $-2$. If you provide the explicit equation of $c$, I can give the exact values of $k$.