Tangents to ellipse (2 Viewers)

[nrumble42]

Hey guys! Quick question:

Find the equations of the tangents to the ellipse x^2 + 4y^2=9, which are parallel to the line 2x + 3y=0

 

[ProdigyInspired]

IIRC you do implicit differentiation on the ellipse, which allows you to find the gradients of the tangent to the ellipse.

The line's gradient is -2/3, so from differentiating the equation of the ellipse, you are able to find dy/dx which = -2/3. Go from there.

I'm not entirely sure though.

 

[jathu123]

Another possible method:
Since it's parallel to that line, the tangent is in the form of y=-2x/3 + b
Now sub this into the equation of the ellipse to get a quadratic in x. Since the line is a tangent, there is only 1 point of intersection, so there are only 1 solution (1 value of x) thus ∆=0. By doing this, you can solve for b

 

[si2136]

Another possible method:
Since it's parallel to that line, the tangent is in the form of y=-2x/3 + b
Now sub this into the equation of the ellipse to get a quadratic in x. Since the line is a tangent, there is only 1 point of intersection, so there are only 1 solution (1 value of x) thus ∆=0. By doing this, you can solve for b

Cheers, that method works rlly well.

 

[Drongoski]

b = 5/2 or -5/2

So the two tangents are:

y = -2x/3 + 5/2

y = -2x/3 - 5/2

 

[nrumble42]

could someone pls show their working out for me??

 

[nrumble42]

nevermind guys haha. I got there