# Lesson Graphing of ellipses

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 Algebra: Conic sections - ellipse, parabola, hyperbola Solvers Lessons Answers archive Quiz In Depth
 This Lesson (Graphing of ellipses) was created by by Alwayscheerful(414)  : View Source, ShowAbout Alwayscheerful: I'm available as an online paid tutor if anyone need extensive 1 on 1 help. =) Ellipses are actually very special cases of circles. All we need to get started is the standard form of an ellipse and that is: REMEMBER: The right side of the equation must be 1 in order to be in standard form. The point (h,k) is most commonly referred to as the CENTER. In order to graph an ellipse, you need 4 points: Right point (h+a,k) Left point (h-a,k) Top point (h,k+b) Bottom point (h,k-b). Note that a is the square root of the number under the x term and is the amount that we move right and left from the center. B is also the square root of the number under the y term and is the amount that we move up or down from the center. EXAMPLE 1 The center of the ellipse will be (-2,4) **CAREFUL WITH SIGNS** a=3, b=5 We can then derive the rest of the points Right point - (h+a,k)=(1,4) Left point - (h-a,k)=(-5,4) Top point - (h,k+b)=(-2,9) Bottom point - (h,k-b)=(-2,-1) Then connect the points with smooth lines, making an oval. EXAMPLE 2 Center: (0,3) a=7, b=2 Right point - (7,3) Left point - (-7,3) Top point - (0,5) Bottom point - (0,1) Then connect the points with smooth lines, making an oval. Now why are ellipses a special case of cirlces? First, let's assume a=b. In that case, we would end up with the following formula. Now since they are equal, we can get rid of the denominators. Seem familiar? **If not, the standard form of a circle is ** :) Hope this helps! This lesson has been accessed 30010 times.