In this page equation of the tangent we are going to see how to find the equation of a tangent to the circle.First let us see the definition.

A tangent to a circle is a straight line which intersects (touches) the circle exactly one point.We can draw only two tangents to a circle from the point outside to a circle.

To get the equation of a tangent at(x₁,y₁) we have to replace x² by xx₁, y² by yy₁ , x as (x + x₁)/2 and y as (y + y₁)/2 in the equation of a circle.

Here we are going to see the examples to find the equation of the tangent to the circle.

**Example 1:**

Find the equation of a tangent to the circle x² + y² = 25 at (4,3).

**Solution:**

As per the procedure, we have to replace x² by xx₁ and y² by yy₁.

Equation of a circle x² + y² = 25

Equation of the tangent

xx₁ + yy₁ = 25

Here (x₁,y₁) is (4,3)

x(4) + y(3) = 25

**4x + 3y = 25**

**Example 2:**

Find the equation of tangent to the circle x² + y² - 4x -3y +12 = 0 at (2,3).

**Solution:**

Equation of the circle x² + y² - 4x -6y +12 = 0

We have to replace x² by xx₁ y² by yy₁,x as (x+x₁)/2 and y as (y +y₁)/2

xx₁ + yy₁ - 4 {(x+x₁)/2} - 6 {(y +y₁)/2} + 12 = 0

Equation of a circle at a point (2,3)

x(2) + y(3) + 2(x +2) -3(y+ 3) + 12 = 0

2x + 3y + 2x + 4 - 3y - 9 + 12 = 0

4x + 16 - 9 = 0

** 4x + 7 = 0**

**Example 3:**

Find the equation of the tangent to x² + y² - 4x -4y -8 = 0 at (-2,-2).

**Solution:**

Equation of the circle x² + y² - 4x -4y -8 = 0

We have to replace x² by xx₁ y² by yy₁,x as (x+x₁)/2 and y as (y +y₁)/2

xx₁ + yy₁ - 4 {(x+x₁)/2} - 4 {(y +y₁)/2} - 8 = 0

Equation of a circle at a point (-2,-2)

x(-2) + y(-2) + 2(x -2) -2(y - 2) -8 = 0

-2x - 2y + 2x - 4 - 2y + 4 - 8 = 0

-4y - 8 = 0

4y + 8 = 0

** y + 2 = 0**

**Related Topics**

**Length of the tangent to a circle****Family of circles****Orthogonal circles****Section formula****Area of triangle****Area of triangle worksheets****Area of quadrilateral****Centroid****Centroid of the triangle worksheets****Finding missing vertex using centroid worksheet****Midpoint****Distance between two points****Distance between two points worksheet****Slope of the line****Equation of the line****Equation of line using two points worksheet****Equation of the line using point and slope worksheets****Point of intersection of two lines****Point of intersection Worksheets****concurrency of straight line****Concurrency of straight lines worksheet****Circumcentre of a triangle****Circumcentre of Triangle Worksheet****Orthocentre of a triangle****Orthocentre of Triangle Worksheet****Incentre of a triangle****Locus****Perpendicular distance****Angle between two straight lines****Equation of a circle****With center and radius****With endpoints of a diameter****Equation of a circle passing though three points****Parabola****Ellipse**

After having gone through the stuff given above, we hope that the students would have understood "Equation of the tangent"

Apart from the stuff given above, if you want to know more about "Equation of the tangent", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Time and work word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**