# Math Assignment Help With Point Of Contact Of A line And A Parabola

## 7.5.8 Point of contact of a line and a parabola:

The point of contact of a line y = m*x* + (a/m) with parabola y^{2} = 4a*x* is given by;

**Example: **Find the equation of the tangent to the parabola y^{2} = 9*x*, passing through (4, 10). Find its point of contact.

**Solution;** equation of parabola: y^{2} = 9*x*

a = 9/4

let the equation of tangent be

** y = m x + a/m**

y = m*x* + 9/4m

as it passes through (4, 10),

10 = 4m + 9/4m

16m^{2} – 40m + 9 = 0

(4m – 1)(4m – 9) = 0

Therefore,

m = 1/4 or m = 9/4

putting the values of m, the required equation of tangents are;

*x* – 4y + 36 = 0

9*x* – 4y + 4 = 0

Putting the values of m in

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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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