How do I solve this question?
Find the equations of both the tangent lines to the ellipse x^2 + 4y^2 = 36 that pass through the point (12, 3).
There is supposed to be 2 tangent lines, a horizontal and non-horizontal one.
Thank you in advance!
How do I solve this question?
Find the equations of both the tangent lines to the ellipse x^2 + 4y^2 = 36 that pass through the point (12, 3).
There is supposed to be 2 tangent lines, a horizontal and non-horizontal one.
Thank you in advance!
The second you hear tangent line, think derivative. Since this has a in it, we're going to differentiate implicity
Moving stuff around,
So the slopes of our lines must have the form above to be tangent
Now we have 1 point, so let's find the toher point
Points on the elipse are represented by or
And slope=
Sooooo,
The derivative equation must equal the slope between the 2 points and lets use our formulas to plug in for y
And don't forget that the y values can be represented 2 ways (+ and -)
Solving both of those will get you your x values, and then to get your y's remember to keep to + and -'s straight
Then the equation of the tangent lines will be
Of course, you already said 1 tangent line will be horizontal, and you know the point it goes through, so you can get that equation almost without thinking