Question

4. A curve C in R2 begins at (-1, 1) and ends at (6,-4). It consists of 4 curvesC₁, C2, C3 and C4. Curve C₁ goes along the parabola y = x² line segment from (-1, 1) and endsat (2,4). It involves a parameter t with 0 ≤ t ≤ 3. • Curve C₂ goes along the lower part of the circle of radius 2 center at (4, 4) from St≤ 2T.(2, 4) to (6,4). It involves a parameter t with \text { - Curve } C_{3} \text { goes the left half of the ellipse with equation } \frac{(x-6)^{2}}{4}+\frac{y^{2}}{16}=1 \text { from } (6,4) \text { to }(6,-4) \text {. It involves a parameter } t \text { from } \frac{\pi}{2} \text { to } \frac{3 \pi}{2} \text {. } -) Give a sketch of the curve C. (1 point) b) Give the parametrization of each of the curves C₁, C₂ and C3. Don't forget that your parametrization must satisfy the given intervals for the param-eter t. Show your work. (3 points)

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