# Math Assignment Help With Position Of A Point With Respect To Parabola

## 7.5.5 Position of a point with respect to parabola

Let a parabola with equation

y^{2} = 4a*x*

and P(*x*1, y1) be a point in the plane.

PR is perpendicular to OX meeting parabola at point Q. co-ordinates of point Q are (*x*2, y2).

Since, point Q lies on y2 = 4a*x*

Hence,

y2^{2} = 4a*x*

PR>QR, PR = QR or PR<QR

i.e.

PR^{2}>QR^{2}, PR^{2} = QR^{2} or PR2<QR^{2}

i.e.

y1^{2} > y2^{2}, y1^{2} = y2^{2} or y1^{2} < y2^{2}

y1^{2} > 4a*x1*, y1^{2} = 4a*x*1 or y1^{2} < 4a*x*1 respectively.

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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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