Ellipse and tangent intersect: x^2 / 9 + y^2 / 25 = 1

[ka923]

I have already done question 3A,
so this is my attempt so far at 3B
i substituted 4x+k in to y^2
then I got (4x+k)^2=25
then 4x+k=+-5, after that i made k the subject which gave me k=+-5-4x
beyond this point i have no idea what i was doing so i attempted to swap in the value of x=+-3 into the equation but doing so gave me a range of different values, please help thanks

P.S if you know any good revision sites for these questions or general conic section please include it in your answer, thanks

 

[Deleted member 4993]

View attachment 10325
I have already done question 3A,
so this is my attempt so far at 3B
i substituted 4x+k in to y^2
then I got (4x+k)^2=25 ........................Incorrect

x^2/9 + (4x+k)^2/25 = 1

(5x)^2 + (12x+ 3k)^2 = 225

169 x^2 + 72kx + (9k^2-225) = 0

For two distinct real points of intersection:

(72k)^2 - 4 * 169 * (9k^2 -225) >0

Now continue...

then 4x+k=+-5, after that i made k the subject which gave me k=+-5-4x
beyond this point i have no idea what i was doing so i attempted to swap in the value of x=+-3 into the equation but doing so gave me a range of different values, please help thanks

P.S if you know any good revision sites for these questions or general conic section please include it in your answer, thanks

View attachment 10325