# Circles

## Circle Examples

Here you will learn some circle examples for better understanding of circle concepts. Example 1 : Find the equation of the normal to the circle $$x^2 + y^2 – 5x + 2y -48$$ = 0 at the point (5,6). Solution : Since the normal to the circle always passes through the centre so the equation …

## Equation of Family of Circle – Director Circle

Here you will learn equation of family of circle and director circle and equation of chord of contact of circle. Family of Circle (a)  The equation of the family of circles passing through the point of intersection of two circles $$S_1$$ = 0 & $$S_2$$ = 0 is : $$S_1$$ + K$$S_2$$ = 0    …

## Common Tangent to Two Circles – Direct & Transverse

Here you will learn common tangent to two circles i.e direct and transverse common tangents and orthogonal circles condition. Let’s begin – Common Tangent to Two Circles Let two circles $$C_1$$ and $$C_2$$ and radii, $$r_1$$ and $$r_2$$ and $$C_1$$$$C_2$$ is the distance between their centres then : (a)  Both circles will touch : (i)  …

## Diameter Form of Circle – Parametric Equation & Example

Diameter Form of Circle The equation of the circle drawn on the straight line joining two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is ($$x-x_1$$)($$x-x_2$$) + ($$y-y_1$$)($$y-y_2$$) = 0. This is known as diameter form of circle. where $$(x_1, y_1)$$ and $$(x_2, y_2)$$ are coordinates of two ends of diameter of circle. Note – If the …

## How to Find Equation of Normal to Circle

The normal at a point is the straight line which is perpendicular to the tangent to circle at the point of contact. Normal at a point of the circle passes through the center of circle. Here, you will learn how to find equation of normal to circle with example. Equation of Normal to Circle : …

## Equation of Tangent to a Circle – Condition of Tangency

When a straight line meet a circle on two coincident points then it is called the tangent to a circle. Here, you will learn condition of line to be a tangent  to a circle and equation of tangent to a circle with example. Condition of Tangency : The line L = 0 touches the circle …

## General Equation of the Circle | Standard Form of Circle

What is a Circle ? A circle is the locus of a point which moves in a plane in such way that its distance from a fixed point(in the same given plane) remains constant. The fixed point is called center of circle and the constant distance is called radius of the circle. The general equation …