Conics Question Help Please! (1 Viewer)

[a1079atw]

Find the equation of the tangents drawn from the point (6, –2) to the ellipse 4x² + 9y² = 36.

Thanks!

 

[esaitchkay]

you can either:
i) use the equation of tangent for an ellipse
and then just sub in (6,-2) as x1 and y1, a=3 and b=2

or if that's unknown (or you don't know how to find it yet)
ii) implicitly differentiate the equation ( http://www.sosmath.com/calculus/diff/der05/der05.html ) - dy/dx will give you the gradient; sub the point (6,-2) in.
then just use point-gradient formula: y-y1=dy/dx(x-x1)

ii) is the method you use to find the result in i)

oops I read the question wrong. LOL
I suppose you can just find the chord of contact where (x0,y0) is (6,-2) and then find the point of intersection (make y the subject and sub the equation into the ellipse) and sub that into the tangent to ellipse equation. Here's what I came up with: https://www.dropbox.com/s/5wfhk56i9klvmx0/Scan0004.jpg but hopefully someone has a shorter and smarter method haha.

 

[dunjaaa]

Just a tip, with a sketch, you would of been able to determine one of the tangents straight away (y=-2)

 

[a1079atw]

you can either:
i) use the equation of tangent for an ellipse
and then just sub in (6,-2) as x1 and y1, a=3 and b=2

or if that's unknown (or you don't know how to find it yet)
ii) implicitly differentiate the equation ( http://www.sosmath.com/calculus/diff/der05/der05.html ) - dy/dx will give you the gradient; sub the point (6,-2) in.
then just use point-gradient formula: y-y1=dy/dx(x-x1)

ii) is the method you use to find the result in i)

oops I read the question wrong. LOL
I suppose you can just find the chord of contact where (x0,y0) is (6,-2) and then find the point of intersection (make y the subject and sub the equation into the ellipse) and sub that into the tangent to ellipse equation. Here's what I came up with: https://www.dropbox.com/s/5wfhk56i9klvmx0/Scan0004.jpg but hopefully someone has a shorter and smarter method haha.

Thank you! I like your way of setting out the solution, clear and easy to follow.

 

[a1079atw]

Just a tip, with a sketch, you would of been able to determine one of the tangents straight away (y=-2)

Wow I didn't realise that, thanks for the tip!