## How do you solve the family of a circle?

The equation is given by (x-h)2 + (y-k)2 = r2. Here (h, k) is fixed and r is a varying parameter. This is the equation of the family of concentric circles.

**What is the differential equation of family of circles?**

General Equation of Circle (π₯βπ)^2+(π¦βπ)^2=π^2 where Centre at (π , π) and Radius is r If circle touches y-axis at origin, Center will be at x-axis So, Center = (a, 0) & Radius = a Thus, equation of circle becomes (π₯βπ)^2+(π¦β0)^2=π^2 (π₯βπ)^2+π¦^2=π^2 π₯^2+π^2β2ππ₯+π¦^2=π^2 π₯^2β2ππ₯+π¦^2=π^2βπ^2 π₯^2β2ππ₯+π¦^2=0 2ππ₯=π₯^2+π¦^2 …

### How do you calculate circle problems?

We know that the general equation for a circle is ( x – h )^2 + ( y – k )^2 = r^2, where ( h, k ) is the center and r is the radius.

**What are different types of circles?**

Types of Circles

- Concentric Circles. When two or more circles have a common center, then these circles are called concentric circles.
- Contact of Circles. When the outer surfaces of two circles are touching, it is known as contact of circles.
- Orthogonal Circles.

## What are the 2 points of circle?

A circle is the set of all points in a plane at a given distance (called the radius ) from a given point (called the center.) A line segment connecting two points on the circle and going through the center is called a diameter of the circle.

**Is a diameter a special chord?**

A chord is a line segment with both endpoints on the circle. The diameter is a special chord that passes through the center of the circle. The diameter would be the longest chord in the circle.

### Which one of the following is the differential equation of the system of circles touching the y axis?

xΒ²βyΒ²+2xydy/dx=0.

**What is the differential equation of the family of parabolas having their vertices at the origin?**

The differential equation of family of parabolas with foci at the origin and axis is y=0.

## What is the standard form of circle?

Standard form for the equation of a circle is (xβh)2+(yβk)2=r2. The center is (h,k) and the radius measures r units. To graph a circle mark points r units up, down, left, and right from the center.

**What is the equation of a circle with center (- 2 3?**

Summary: The equation of the circle with center (2, -3) and a radius of 4 is x2 + y2 – 4x + 6y = 3.

### What are real life examples of circles?

Some of the real-world examples of circles are:

- The wheel of a bicycle.
- Coin.
- Dinner plate.
- Wall clock.
- Ferris wheels.

**What is a family of circles?**

Is this page helpful? A circle is a closed shape simple figure in which all the points lying on the surface of the circle joining its centre are equal and known as radius of the circle. A huge collection of circles is called a family of circles.

## What is the equation of the family of circles touching it?

Here, we can have two sub-cases according as whether the line is parallel to x -axis or y-axis. If this line through (x 1, y 1 ) is parallel to x-axis, then the equation of the family of circles touching it at (x1, y1) becomes (x β x 1) 2 + (y β y 1) 2 + K (y β y 1) = 0.

**How do you find the family of circles that touch y-axis?**

The equation of the family of circles which touch the line y β y 1 = m (x β x1) at (x1, y1) for any values of m is (x β x1)2 + (y β y1)2 + Ξ»[ (y β y1) β m (x β x1)] = 0. Here, we can have two sub-cases according as whether the line is parallel to x -axis or y-axis.

### How do you find the family of circles passing through intersection?

Equation of Family of circles passing through intersection of two circles S1 = 0 and S2 = 0. The general equation of the family of circles passing through the intersection of S1 and S2 in given by S1 + kS2 = 0, where k β -1.