# Math Assignment Help With General Equation Of Parabola

## 7.5.4 General equation of parabola:

Let F(h, k) be the focus of the parabola and let the equation of its directrix be;

A*x* + by + c = 0

Let P(*x*, y) be a point on the parabola and PM be the perpendicular from P on the directrix.

PF = PM

√(*x – *h)^{2} + (y – k)^{2} = a*x* + by + c

√(a^{2} + b^{2})

*x* – h)^{2} + (y – k)^{2} = (a*x* + by + c)^{2}

a^{2} + b^{2}

(a^{2} + b^{2}) [(*x *– h)^{2} + (y – k)^{2}] = (a*x* + by + c)^{2}

On solving the above equation we get;

**(b x – ay)^{2} + 2gx + 2fy + d = 0**

This is the general form of parabolic equation.

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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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