Intersection of a line and a parabola

Intersection of line and Tangent to the parabola

Intersection of Ellipse with Parabola

Parabola- common tangent OF two curves || Point OF intersection OF tangents OF a parabola || Equation OF normal OF a parabola

Intersection of Parabola with Parabola

LetS={(x,y)|x^(2)+2xy+y^(2)-3x-3y+2=0}, thenS vdots(A) consists of two coincident lines.(B) consists of two parallel lines which are not coincident.(C) consists of two intersecting lines.(D) is a parabola.

Find limit of the ratio of the area of the triangle formed by the origin and intersection points of the parabola y=4x^2 and the line y=a^2 to the area between the parabola and the line as a approaches to zero.

Find limit of the ratio of the area of the triangle formed by the origin and intersection points of the parabola y=4x^2 and the line y=a^2 to the area between the parabola and the line as a approaches to zero.