# Ellipse Identification

Calculus Level 5

An ellipse having the equation,

$\dfrac{(x - h)^2 }{ a^2} +\dfrac{ (y - k)^2 }{ b^2} = 1$

passes through the points $$(7, 2)$$ and $$(-1, 4)$$. It has a slope of $$-4$$ and $$\dfrac{1}{3}$$ at the first point and second point, respectively.

Identify this ellipse, by finding $$a, b, h, k$$. Enter your answer as $$a + b + h + k$$.