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Hyperbola Examples by mes

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hive-128780 · @mes · (edited)
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Hyperbola Examples
https://youtu.be/LvccUMFrY3k

In this video I go through some important examples in understanding how to sketch and obtain the equation of a hyperbola.

Download video notes: https://1drv.ms/u/s!As32ynv0LoaIicg9gFI6sv6jFFHZBw?e=Geqcdf

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# Hyperbola Examples

![Hyperbola Examples Resized AI.jpg](https://files.peakd.com/file/peakd-hive/mes/23xpVcvU5WB27hnypHpy7e1RVbqx9crzn5XBp99QdkgjFBFCZYQw5kYR2RKzskxjJ3do6.jpg)

# Hyperbola Review

![image.png](https://files.peakd.com/file/peakd-hive/mes/23sxpXQpjSzuy5spjAvGMGtTq6f21UUVvrw1feV7vHtyxNP9x34LmnhnEBUVB3mXZZjD2.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/Eo4KDWWrcwLy1npSvsEffDLnkiFw89f6XQK2uMmReTA67p4AnV2qdgvLCwfHgvMkb3e.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHdQDGn4Zi8BHoGv8P3saarUgjiZeA5pb79dBMYNjDwpwKaoJXiDXGgjcSJhGYtbp66.png)

# Example 1

Sketch the hyperbola 9x<sup>2</sup> - 16y<sup>2</sup> = 144

**Solution:**

![image.png](https://files.peakd.com/file/peakd-hive/mes/23sxpXQpjKtYU1vvje5JT2WEF8u5CcN5jQ4JcnBSebnTbXb4r8QLBZhrMgmdZBCMvjsYx.png)

# Example 2

Find the equation of a hyperbola whose vertices are (0, ±1) and asymptotes lines y = ±2x.

**Solution:**

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9ym7bkYzFtvLQ4WjfgqaFWC2CnByXwXYpDngNco8A8uYrpxigy7xM2kG9XB9YT5.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8EjqhG1MufxnbVsrFSgcJctBmiFZLEPd5LwHszgeJ2yRikeHL2hcTm9w1FR6LSPutt.png)

# Example 3

Sketch the hyperbola 9x<sup>2</sup> - 4y<sup>2</sup> - 72x + 8y + 176 = 0.

**Solution:**

![image.png](https://files.peakd.com/file/peakd-hive/mes/23sxozwpQhmZhy9KiUXmUhtK8ymAQcE1DAMjkzWmurNJ6y3jiPUV5YcK4RhfEBEATW9mS.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23tHbr9yksdJqZeug7ftKW94YxRpmpLdZTRQ98S6uFAXwTCLzDJjcVPXR7MwJYMmnVwxh.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23sxozwpQvqGUZPYgFsjqdySzcm6ryfoY7KeaR7fcRTWPxUNRDzQUdjvw8ar762WrKFix.png)

![image.png](https://files.peakd.com/file/peakd-hive/mes/23t8DBnQFPMM2GEGNMWhUV6S3nPfHQ3hiscECuGxit7UrjZ66knqJskDs5ccQbK181FnU.png)
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