CIRCLES

dylanp0505

The line with the equation y=kx, where k is a constant, cuts C at two points

(b) Find the range of values of k

Reply 1

davros

Original post by dylanp0505

The line with the equation y=kx, where k is a constant, cuts C at two points

(b) Find the range of values of k

do you have more info, like the equation of C? Is there a part (a) you've omitted?

Reply 2

dylanp0505

x^2 + y^2 -6x + 10y +9=0

Reply 3

dylanp0505

For part a I got the radius to be 5
And the centre of the circle to be (3,-5)

Reply 4

mqb2766

You could sub y=kx into the circle equation and solve, or sketch the circle and a bit of reasoning.

(edited 10 months ago)

Reply 5

JaCey04

plug y = kx into the C equation. You will get a quadratic with x. You know that has two solutions since the line cuts the circle twice so use b^2-4ac>0

thank you

Im sure you solved it the algebraic / discriminant way, but as an alternative using geometry
https://www.desmos.com/calculator/mxbxijodya
Then for the gradient of the 2nd tangent (not x - axis), the circle centre - origin line has a gradient of -5/3, so using the tan double angle formula, your gradient of the tangent (k) is
2*(-5/3) / (1 - (-5/3)^2) = 15/8

(edited 10 months ago)