From the point A(0,3) on the circle x^2+4 x+(y-3)^2=0, a chord A B is drawn and extended to a po

step 1 So in this question we have to give an equation of circle is x to square plus y square plus 4x p

From the point A(0,3) on the circle x^2+4 x+(y-3)^2=0, a...

Key Concepts

Section Formula and Homothety

The section formula helps determine the coordinates of a point that divides a line segment in a given ratio. Homothety (or dilation) is a specific type of transformation that scales figures from a fixed center point. In many geometric locus problems, applying a homothety with a fixed center transforms one curve into another by scaling distances, preserving the shape while altering the size.

Chords

A chord is a line segment whose endpoints lie on a circle. In problems involving chords, the relationships between the endpoints, the chord’s length, and its position relative to the circle’s center often play a key role, especially when chords are extended or divided in a specific ratio.

Coordinate Geometry Transformations

Coordinate geometry transformations, such as translations, dilations, and rotations, are used to move or scale figures in the plane while preserving their geometric properties. These techniques are instrumental in deriving the locus of points resulting from specific geometric constructions or ratios applied to known curves.

Locus

A locus is the set of all points that satisfy a particular condition or a set of conditions. In coordinate geometry, defining a locus means finding an equation or rule that every point on that curve or region must obey, thereby describing its geometric nature.

Circle Equation

A circle equation in the Cartesian plane represents all points that are at a fixed distance (the radius) from a fixed point (the center). Understanding the standard and completed square forms of the circle equation is essential for analyzing its properties and for performing transformations.

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