GATE 2023 BT – Question 35
The distance between the two points of intersection of $x^2+y=7$ and $x+y=7$ (rounded off to two decimal places) is ____________.
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Correct answer: 1.40 to 1.42
Explanation
**Step 1: find the intersection points.** Subtract the equations, or eliminate $y=7-x$ from $x^2+y=7$:
$$x^2+(7-x)=7\;\Rightarrow\;x^2-x=0\;\Rightarrow\;x(x-1)=0 .$$
So $x=0$ or $x=1$. The points are $(0,7)$ and $(1,6)$.
**Step 2: distance.**
$$d=\sqrt{(1-0)^2+(6-7)^2}=\sqrt2=\mathbf{1.41}.$$