# Math Assignment Help With Condition Of Tangency

## 7.5.7 Condition of tangency:

**Theorem:** The condition of tangency states that the line y = m*x* + c touches the parabola y^{2} = 4a*x* at

**c = a/m**

Proof: let y = m*x* + c be the line intersecting the parabola y^{2} = 4a*x*

y^{2} = 4a*x*, y = m*x* + c

(m*x* + c)^{2} = 4a*x*

m^{2} *x*^{2} + c^{2} + 2m*x*c = 4a*x*

m^{2} *x*^{2} +2(mc – 2a)*x* + c2 = 0

The line will touch the parabola if it intersects at one point only. This will happen only when the roots are real and coincident.

For

y = m*x* + c being a tangent to y^{2} = 4a*x*

we must have,

4(mc – 2a)^{2} – 4m^{2}c^{2} = 0

4a^{2} – 4amc = 0

Therefore for all values of **m** the line **y = m x + a/m** is always tangent to the parabola

**y**

^{2}= 4a*x*### Email Based Assignment Help in Condition Of Tangency

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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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