Find the value of `P` such that the vertex of `y=x^2+2p x+13` is 4 units above the x-axis.

Find the value of P such that the vertex of y=x^(2)+2px+13 is 4 units above the x-axis. (a) +-2 (b) 4(c)+-3 (d ) 5

Find the area bounded by the curves x^(2)+y^(2)=25,4y=|4-x^(2)|, and x=0 above the x-axis.

Find the angle of intersection of the curves y^(2)=4x,x=4y at P, but P is not the origin

AP is perpendicular to PB, where A is the vertex of the parabola y^(2)=4x and P is on the parabola.B is on the axis of the parabola. Then find the locus of the centroid of o+PAB .

Evaluate the area bounded by the ellipse (x^2)/(4)+(y^2)/(9)=1 above the x-axis.

Let the line y = mx intersects the curve y^2 = x at P and tangent to y^2 = x at P intersects x-axis at Q. If area ( triangle OPQ) = 4, find m (m gt 0) .

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P(h,k) with the lines y=x and x+y=2 is 4h^(2). Find the locus of the point P.

Find the point P on the parabola y^(2)=4ax such that area bounded by the parabola,the x- axis and the tangent at P equal to that of bourmal by the parabola,the x-axis and the normal at P.

Find the vertex, axis, focus, directrix, tangent at the vertex, and length of the latus rectum of the parabola 2y^(2) + 3y - 4x - 3 = 0 .