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hyperbola.html
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<!DOCTYPE html>
<html lang="en">
<head>
<title>Hyperbola</title>
<link rel="icon" type="image/x-icon" href="./assets/images/favicon.ico">
<link rel="manifest" href="./manifest.json">
<script defer src="katex/katex.min.js"></script>
<script defer src="katex/contrib/auto-render.min.js" onload="renderMathInElement(document.body);"></script>
<link href="katex/katex.min.css" rel="stylesheet">
<style>
@import url(./variable.css);
* {
font-family: "Jost", sans-serif;
background-color: #d5f1f5;
text-align: center;
}
.form__field {
font-family: "Jost", sans-serif;
font-size: 1.2rem !important;
letter-spacing: 0.125rem;
width: 28%;
border: 0;
box-shadow: 0 0 10px black;
outline: 0;
margin-bottom: 1%;
color: black;
background-color: var(--appblack);
padding: 10px;
border-radius: 10px;
}
.btn {
background-color: #d5f1f5;
color: hsl(229, 84%, 12%);
border: 2px solid hsl(229, 84%, 12%);
width: 9%;
height: 46px;
border-radius: 28px;
font-size: 21px;
font-family: "Jost", sans-serif;
color: hsl(229, 84%, 12%);
}
.btn:hover {
background-color: hsl(229, 84%, 12%);
color: white;
}
form {
text-align: center;
}
h4 {
font-size: 28px;
padding: 20px;
font-weight: 800;
color: hsl(229, 84%, 12%);
text-align: center;
}
table,
th,
td {
border: 1px solid black;
margin-left: auto;
margin-right: auto;
}
li {
font-size: 21px;
font-weight: var(--fw-8);
color: var(--oxford-blue);
line-height: 1.3;
}
</style>
</head>
<body>
<!--Calculator code for trivial hyperbola solution ends here-->
<br>
<div class="stopwrap">
<table class="table table-bordered table-dark">
<thead>
<tr>
<th scope="col">\[Equation\]</th>
<th scope="col">\[Graph\]</th>
<th scope="col">\[Focus\]</th>
<th scope="col">\[Length\space of\space LR\]</th>
<th scope="col">\[Directrix\]</th>
<th scope="col">\[Length\space of\space Transverse\space Axis\]</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">\[\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1\]</th>
<td><img src="assets/images/Hyperbola1.webp" class="img-fluid"></td>
<td>\[(±ae,0)\]</td>
<td>\[\frac{2b^2}{a}\]</td>
<td>\[x=±\frac{a}{e}\]</td>
<td>\[2a\]</td>
</tr>
<tr>
<th scope="row">\[\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1\]</th>
<td><img src="assets/images/Hyperbola2.webp" class="img-fluid"></td>
<td>\[(0,±be)\]</td>
<td>\[\frac{2a^2}{b}\]</td>
<td>\[y=±\frac{b}{e}\]</td>
<td>\[2b\]</td>
</tr>
<tr>
<th scope="row">\[{x^2}\space-{y^2}\space={a^2}\]</th>
<td><img src="https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSw5QUDKo9jqVjTyqagOTwt6qgP04QWO60TWw&usqp=CAU"
class="img-fluid"></td>
<td>\[(0, ±a{\sqrt{2}} )\]</td>
<td>\[2a\]</td>
<td>\[x=±\frac{a}{\sqrt{2}}\]</td>
<td>\[2a\]</td>
</tr>
</tbody>
</table>
<h2>Equations of Tangent of Hyperbola</h2>
<table class="table table-bordered table-dark">
<thead>
<tr>
<th scope="col">\[Equation\]</th>
<th scope="col">\[Parametric\space Coordinates\]</th>
<th scope="col">\[Equation\space of\space tangent\]</th>
<th scope="col">\[Condition\space of \space Tangency\]</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">\[\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1\]</th>
<td>\[(asec\theta,btan\theta)\]</td>
<td>\[y=mx±\sqrt{am^2-b^2}\]</td>
<td>\[c=±\sqrt{am^2-b^2}\]</td>
</tr>
<tr>
<th scope="row">\[\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1\]</th>
<td>\[(bsec\theta,atan\theta)\]</td>
<td>\[y=mx±\sqrt{-bm^2+a^2}\]</td>
<td>\[c=±\sqrt{-bm^2+a^2}\]</td>
</tr>
<tr>
<th scope="row">\[{x^2}\space-{y^2}\space={a^2}\]</th>
<td>\[(asec\theta,atan\theta)\]</td>
<td>\[y=mx±\sqrt{am^2-a^2}\]</td>
<td>\[c=±\sqrt{am^2-a^2}\]</td>
</tr>
</tbody>
</table>
<h2>Equations of Normal of Hyperbola</h2>
<table class="table table-bordered table-dark">
<thead>
<tr>
<th scope="col">\[Equation\]</th>
<th scope="col">\[Parametric\space Coordinates\]</th>
<th scope="col">\[Equation\space of\space Normal\]</th>
<th scope="col">\[Condition\space of \space Normality\]</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">\[\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1\]</th>
<td>\[(asec\theta,btan\theta)\]</td>
<td>\[\frac{ax}{sec\theta}+\frac{by}{tan\theta}=a^2+b^2\]</td>
<td>\[c=\frac{m(a^2+b^2)}{\sqrt{a^2-b^2m^2}}\]</td>
</tr>
<tr>
<th scope="row">\[\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1\]</th>
<td>\[(bsec\theta,atan\theta)\]</td>
<td>\[\frac{bx}{sec\theta}+\frac{ay}{tan\theta}=b^2+a^2\]</td>
<td>\[c=\frac{m(b^2-a^2)}{\sqrt{a^2m^2-b^2}}\]</td>
</tr>
<tr>
<th scope="row">\[{x^2}\space-{y^2}\space={a^2}\]</th>
<td>\[(asec\theta,atan\theta)\]</td>
<td>\[\frac{x}{sec\theta}+\frac{y}{tan\theta}=2a\]</td>
<td>\[c=\frac{2am}{\sqrt{1-m^2}}\]</td>
</tr>
</tbody>
</table>
<h2>Equations of Director Circle of Hyperbola</h2>
<table class="table table-bordered table-dark">
<thead>
<tr>
<th scope="col">\[Equation\]</th>
<th scope="col">\[Equation\space of\space Director\space Circle\]</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">\[\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1\]</th>
<td>\[x^2\,+\,y^2\space\,=a^2\,-\,b^2\]</td>
</tr>
<tr>
<th scope="row">\[\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1\]</th>
<td>\[x^2\,+\,y^2\space\,=b^2\,-\,a^2\]</td>
</tr>
</tbody>
</table>
</div>
</body>
</html>