Question

Show that the line x - y = 5 is a tangent to
the ellipse 9x2 + 16y2 = 144. Find the point
of contact.​

Answer 1

HELLO!

The condition of tangency for an ellipse is:

$c^{2} = a^{2}m^{2} + b^{2}$

We basically have to show that this condition is valid.

And, for the point of contact, we can use the direct time saving formula, otherwise you have to solve the line and the ellipse to get the point which is generally not the suggested way.

Check out the attachment for the solution.

Thanks!