Question

Help me please :)
(a) Differentiate the semicircle y =sqrt(169 − x^2) , find the equation of the tangent at P(12, 5), and find the x-intercept and y-intercept of the tangent.
(b) Show that the perpendicular distance from the tangent to the centre equals the radius.
(c) Find the area of the triangle enclosed by the tangent and the two axes.
(d) Find the perimeter of this triangle.

Answer 1

i have gotten the gradient to be -12/5

Answer 2

I have done part (a) and equation is 5y+12x-169=0

Answer 3

First of all, y =169 − x^2 is NOT A SEMICIRCLE it is a PARABOLA...

Answer 4

umm radius is 13? sorry i changed the question

Answer 5

Okay - that makes more sense!

Answer 6

Now do you know the centre of the circle?

Answer 7

is it the origin?

Answer 8

yep, do you know how to get it?

Answer 9

yea ill use the perpendicular formula

Answer 10

now i have gotten the distance to be 13?

Answer 11

you can do it another way:

y = √169-x^2
y^2 = 169 - x^2
y^2 + x^2 = 169

Therefore C (0,0) and r = √169 = 13

Answer 12

Cool, now for part b) do you know how to find the distance between two points,
(0,0) and (12,5) ?

Answer 13

@AonZ @BarbaraKara Can I be of any assistance?

Answer 14

sure :)

Answer 15

What do you need help with atm @AonZ

Answer 16

part (c) so far

Answer 17

it should be ok, i think i can solve this now

Answer 18

So the equation of the tangent line is 5y + 12x - 169 = 0. Is that correct? @AonZ

Answer 19

I think im fine now, thanks :)

Answer 20

well ok. tag me if you need any help.

Answer 21

Sure, will do