query: Find the equations of all tangent lines to the curve $x^2 + 4y^2 = 8$ that pass through the point (−4, 0).
positive_passages.docid: 17545
positive_passages.text: Tangent lines to ellipse from external point
negative_passages.docid: 37478
negative_passages.text: Write the equation of the parabola that has the vertex at point $(5,0)$ and passes through the point $(7,−2)$.
negative_passages.docid: 7158
negative_passages.text: Using implicit differentiation to find a line that is tangent to a curve at a point
negative_passages.docid: 37936
negative_passages.text: Solve for z^8-z^4+1 = 0
negative_passages.docid: 17027
negative_passages.text: Calculating Taylor polynomial of an implicit function given by an equation
negative_passages.docid: 144901
negative_passages.text: Tangent to a circle through a point
negative_passages.docid: 79
negative_passages.text: Find $a$, $b$ and $c$ that satisfy the following equations
negative_passages.docid: 88889
negative_passages.text: Find equation of a plane that passes through point and contains the intersection line of 2 other planes
negative_passages.docid: 157200
negative_passages.text: Roots of a equation on a complex plane
negative_passages.docid: 105280
negative_passages.text: How to find the equation of a parabola given the tangent equations to two points?
negative_passages.docid: 103020
negative_passages.text: Find all integral solutions of $ x^4 + y^4 + z^4 -w^4 = 1995 $
negative_passages.docid: 22112
negative_passages.text: Find all integer solutions to $x^2+4=y^3$.
negative_passages.docid: 64492
negative_passages.text: Where does the curve $x^y = y^x$ intersect itself?
negative_passages.docid: 105825
negative_passages.text: Hard Multivariable Calculus Question: Surfaces
negative_passages.docid: 61548
negative_passages.text: What would be the roots of the derivative of this polynomial
negative_passages.docid: 14520
negative_passages.text: Get the equation of a circle when given 3 points
negative_passages.docid: 41689
negative_passages.text: Find all solutions: $x^2 + 2y^2 = z^2$