91Ó°ÊÓ

Answer: The three basic conic sections are circles, ellipses, and hyperbolas. To sketch them with vertices and foci on the y-axis, follow these steps: 1. Circle: Use the equation \(x^2+y^2=r^2\), choose a radius \(r\), and draw a circle with that radius. Mark the vertices at points \((0, r)\) and \((0, -r)\), and the foci at the origin. 2. Ellipse: Use the equation \(\frac{x^2}{b^2}+\frac{y^2}{a^2}=1\), choose values for \(a\) and \(b\) with \(a > b\), and draw the ellipse. Mark the vertices at points \((0, a)\) and \((0, -a)\), and the foci equidistant from the origin along the y-axis, using the formula \(2\sqrt{a^2-b^2}\). 3. Hyperbola: Use the equation \(\frac{x^2}{b^2}-\frac{y^2}{a^2}=1\), choose values for \(a\) and \(b\), and draw the hyperbola. Mark the vertices at points \((0, a)\) and \((0, -a)\), and the foci at points \((0, c)\) and \((0, -c)\), where \(c=\sqrt{a^2+b^2}\).