Normal: Examples


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 x2­­ + y2 = 25

(i) at the point (4, 3)

(ii) from the point (5, 6)

(iii) of slope = 3

Solution (i) Using the first form from the previous lesson­, the required equation will be y/3 = x/4 or 3x – 4y = 0

(ii) Using the second form from the previous lesson­, the required equation will be y/6 = x/5 or 6x – 5y = 0

(iii) Using the third form from 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 x2­­ + y2 – 6x – 8y = 0.

(i) at the point (6, 8)

(ii) from the point (1, 6)

(iii) of slope = 4

Solution (i) Using the fourth form from 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 from 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 from 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.

Leave a comment