Graphing Conic Sections

Exercises 63-68 give ...

Question

Graphing Conic Sections

Exercises 63-68 give equations for conic sections and tell how many units up or down and to the right or left each curve is to be shifted. Find an equation for the new conic section, and find the new foci, vertices, centers, and asymptotes, as appropriate. If the curve is a parabola, find the new directrix as well.

x²/169 + y²/144 = 1, right 5, up 12

Accepted Answer

Given the ellipse X2 divided by 100 plus Y2 divided by 25 equals 1, shift it right 8 units and down 4 units. Write the equation for the new ellipse and find its center, vertices, co-vertices, and fosite. Now, let's first find a new equation. We're just shifting it around, so we'll first shift it right 8. This means we replace X with X minus 8. We'll put square divided by 100. We do the same for y. Now shifting down, so we'll put y + 4 squad divided by 25. This equals 1 These are Our new equation. Now, we can find our sinner. Since the original sinner was already 00, we just add 8 and subtract 4, giving our new sinner, which is given by HK. As 8-4. From here we can find the vertices. Now, this is a horizontally oriented ellipse. So, we will add A to our H coordinate. Our vertices then will just be plus or minus a. 0. But then we apply our shift. Meaning we end up getting. 8 plus or minus 10. -4 This gives us two vertices of 18-4. And 2, -4. Now our co vertices. Will be given by 0 plus or minus b but because it's shifted. We will write this then As 8, -4 plus or minus 5. We end up getting 8s. -9 and. 81, as our two covertices. Finally, we just need our fossa. We just need to find C. So fossa are given by plus or minus C0, because this is horizontally oriented. And so we just need to find C first. We have C2 equals A2 minus B2, which is 100 minus 25. C2 then equals 75, which means C simplifies to 5 squares of 3. This means our hosa. Will be 8 plus or minus 5 squares of 3 and -4 when accounting for the shift. And since those don't simplify it, we can just leave it. We finally have all of our answers. We have our new equation. Our center Our vertices Covertices and Rhosite. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

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