# An ellipsis

#### Integrator

Good evening to all,

Let $$\displaystyle M$$ be a point outside the ellipse $$\displaystyle ϵ (a, b, O)$$, and $$\displaystyle MT_1$$ and $$\displaystyle MT_2$$ are the two tangent lines to the ellipse. Line $$\displaystyle MO$$ intersects the ellipse at points $$\displaystyle N$$ and $$\displaystyle P$$. Calculate:

1)$$\displaystyle | MT_1^2 - MT_2^2 |$$

2) $$\displaystyle | MN⋅MP - MT_1^2 |$$

3) $$\displaystyle | MN⋅MP - MT_2^2 |$$

All the best,

integrator

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#### v8archie

Math Team
And the ellipsis…?