The graph of the equation 2x2 + xy + y2 = 4 is the tilted ellipse pictured below; i. e. the points (x, y) in the plane that satisfy the equation yield the pictured ellipse. the point p=(1,-2) on the ellipse and the tangent through p are pictured below. a line that is tangent to an ellipse does not intersect the ellipse in any other point. we can use this fact to determine the slope of the tangent line.

The slope of the tangent at point is

Further explanation:

Given:

The equation of the ellipse is

The point is on the ellipse and the tangent.

Explanation:

The given equation of the ellipse is

Now differentiate the equation of ellipse with respect to .

Further solve the above equation.

Substitute for and for y in equation

The slope of the tangent at point is

Learn more:

1. Learn more about inverse of the functionhttps://link.

2. Learn more about equation of circle link.

3. Learn more about range and domain of the function link

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Application of derivatives

Keywords: Derivative, graph of the equation, 2x2+xy+y2=4, ellipse, tangent, equation yield, pictured ellipse, line, intersect, slope, normal, slope of tangent line.

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral