This lesson will a cover a few solved examples relating to equations of a normal to a circle.

**Example 1. **Find the equation of the normal to the circle x^{2 }+ y^{2} = 25

(i) at the point (4, 3)

(ii) from the point (5, 6)

(iii) of slope = 3

**Solution. **(i) Using the first case in the previous lesson**, the required equation will be **y/3 = x/4** or **3x – 4y = 0**

(ii) Using the second case in the previous lesson_{}, the required equation will be **y/6 = x/5** or **6x – 5y = 0**

(iii) Using the third form in the previous lesson_{}, the required equation will be **y = 3x** or **3x – y = 0**

**Example 2. **Find the equation of the normal to the circle x^{2 }+ y^{2} – 6x – 8y = 0.

(i) at the point (6, 8)

(ii) from the point (1, 6)

(iii) of slope = 4

**Solution. **(i) Using the fourth case in the previous lesson**, the required equation will be **(y – 8)/(8 – 4) = (x – 6)/(6 – 3)** or **4x – 3y = 0.**

(ii) Using the fifth form in the previous lesson_{}, the required equation will be **(y – 6)/(6 – 4) = (x – 1)/(1 – 3)** or **x + y = 7.**

(iii) Using the sixth form in the previous lesson_{}, the required equation will be **y – 4 = 4(x – 3)** or **4x – y – 8 = 0.**

As you can see, there isn’t much thinking involved in the above problems. All you need to remember is – “A normal to a circle will always pass through its center”.

That’ll be all for this lesson. The next one will talk about shortest distance between two curves.