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Assume that the constants [math]a[/math], [math]b[/math], [math]c[/math], [math]d[/math], and [math]e[/math] are such that [math]ax^2 + by^2 + cx + dy + e = 0[/math] is an equation of an ellipse. Consider a point [math](x_1,y_1)[/math] on this ellipse.

• Find the slope of the tangent to the graph at [math](x_1,y_1)[/math].
• Write an equation of the tangent line in (a).
• Show that [math]axx_1 + byy_1 + \frac12c(x+x_1) + \frac12d(y+y_1) + e = 0[/math] is an equation of the tangent line.