Circle problems...

[12345678]

Hello, I was wondering if somebody could spot the mistakes in my working for these questions- I know I’m close but keep getting the answer slightly wrong.

1. ‘Find the equation of the normal to the circle X² + Y² - 4X – 30 = 0, at the point (7,3)’.
   I started off by finding the centre of the circle…
   Completing the square gives (X + 2)² + (Y + 0)²,
   Meaning the centre of the circle is (2,0)
   I then found the gradient of the radius line: (3 – 0) / (7-2) = 3/5
   Subbing this into Y = MX + C…
   3 = 3/5X + C
   3 = 3/5 (7) + C
   15 = 21 + C
   So C = -6.
   I then wrote my final equation as: Y = 3/5X – 6.
   However, the textbook writes it as: 3X – 5Y – 6 = 0.
   I’m under the impression that you times both sides by the same thing, so if you were to get rid of the 5, it would be 5Y = 3X – 30, rearranging to 3X – 5Y – 30 = 0, is my knowledge wrong?

 

[12345678]

Try this again...if you end up with C = -6/5, then you're correct :wink:
Perhaps you needed another coffee

Gradient = 3/5 , X = 7, Y = 3

Y = MX + C

3 = 3/5(7) + C

15 = 21 + 5C

5C = -6

C = -6/5 --- Cheers, keep forgetting simple steps when I keep getting stuff wrong

I know its not the same question, but can you see how : Y = 1/3X can equal X +3Y = 0?
Getting rid of the fraction results in 3Y = X, so this gives X - 3Y = 0?