# Math Assignment Help With Intersection Of A Line And Hyperbola

## 7.6.6 Intersection of a line and Hyperbola:

The only condition for a line y = m*x* + c to be tangent on hyperbola *x*^{2} + y^{2} is;

a^{2} b^{2}

c = ± √a^{2}m^{2} – b^{2}

**Example**: Find the point of contact of a line 5*x* + 2y = 9 touching the hyperbola *x ^{2}* – 9y

^{2}= 9.

**Solution:** The given line is 5*x* + 12y = 9 ….(i)

The given hyperbola is *x ^{2}* – 9y

^{2}= 9. ….(ii)

9*x*^{2} – 90*x* +225 = 0

*X*^{2} – 10 *x *+ 25 = 0

(*x* – 5)^{2} = 0

*X* = 5, 5 are the two coincident roots.

Putting *x = 5* in (i) we get y = -(4/3)

Therefore,

The point of contact is (5, -4/3)

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

- Introduction To Conic Sections
- Eccentricity
- Parameters Of Conic Section
- Parabola
- Forms Of Parabola
- General Equation Of Parabola
- Position Of A Point With Respect To Parabola
- Equation Of A Tangent And Normal At A Point
- Condition Of Tangency
- Point Of Contact Of A Line And A Parabola
- Ellipse
- Ellipse Properties

- Vertical Form Of Ellipse
- General Equation Of Ellipse
- Position Of A Point With Respect To An Ellipse
- Eccentric Angle
- Equations Of Tangent And Normal To An Ellipse
- Condition Of A Line To Touch An Ellipse
- 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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