# Math Assignment Help With Tangent And Normal At A Point On Hyperbola

## 7.6.5 Tangent and Normal at a point on Hyperbola:

The equation of a tangent at a point P(*x*1, y1) of the hyperbola ** x^{2} -y^{2} = 1 **is given by ;

**a ^{2} b^{2}**

*xx***1**** - yy1 = 1**

**a ^{2} b^{2}**

and the equation of normal at this point is given by;

*x – x***1 ****- y - y1 = 1 **

*x1 ***/a ^{2} y1/ b^{2}**

**Example:** Find the equation of tangent and normal to the hyperbola 16*x*^{2} – 25y^{2} = 400 at the point (3, 2).

Solution: Equation of the given hyperbola

*x*^{2}- y^{2} = 1

25 16

Therefore, the equation of tangent to the hyperbola at (3,2) is;

*xx*1 - yy1 = 1

a^{2} b^{2}

a^{2} = 9 and b^{2} = 4; *x1* = 3 and y1 = 2

3*x* - 2y = 1 or *x* - y = 1

9 4 3 2

Or

2*x* – 3y = 6

The equation of the normal at (3, 2) is

(*x* – 3) + (y – 2)

3/9 2/4

3*x* + 2y = 5

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### Following are some of the topics in Conic Sections-Parabola, Hyperbola And Ellipse in which we provide help:

- Vertical Form Of Ellipse
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- Position Of A Point With Respect To An Ellipse
- Eccentric Angle
- Equations Of Tangent And Normal To An Ellipse
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- Hyperbola
- Forms Of Hyperbola
- General Equation Of Hyperbola
- Tangent And Normal At A Point On Hyperbola
- Intersection Of A Line And Hyperbola
- Equation Of A Tangent From A Point Outside The Hyperbola

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