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.