The parabola `y^2=4x` and the circle having its center at 6, 5) intersect at right angle. Then find the possible points of intersection of these curves.

Find the maximum number of points of intersection of 6 circles.

The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at right angles. Then the equation of the circle through the points of intersection of two conics is

Find the angle of intersection of the curves x y=a^2a n dx^2+y^2=2a^2

Find the angle of intersection of the curves 2y^(2)=x^(3)andy^(2)=32x .

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

Consider the parabola y^(2) = 4ax (i) Write the equation of the rectum and obtain the x co-ordinates of the point of intersection of latus rectum and the parabola. (ii) Find the area of the parabola bounded by the latus rectum.

If line x-2y-1=0 intersects parabola y^(2)=4x at P and Q, then find the point of intersection of normals at P and Q.

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

If the tangents are drawn to the circle x^2+y^2=12 at the point where it meets the circle x^2+y^2-5x+3y-2=0, then find the point of intersection of these tangents.