Consider a hyperbola H : `x^(2)-y^(2)` =k and a parabola `P:y=x^(2)` then identify the correct statements(S)

Consider the parabola y=x^2 The shaded area is

Consider the hyperbola H: x^(2)-y^(2)=1 and a circle S with centre N(x_(2),0) . Suppose that H ans S touch each other at a point P(x_(1),y_(1)) with x_(1)gt1 and y_(1)gt0 . The common tangent to H ans S at P intersects the x-axis at point M. If (l, m) is the centroid of the triangle PMN, then the correct expression(s) is (are)-

Consider the circles S_(1):x^(2)+y^(2)=4 and S_(2):x^(2)+y^(2)-2x-4y+4=0 which of the following statements are correct?

If (x-h)^(2)=4a(y-k) represents a parabola then ends of latusrectum

Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They intersect at P and Q in first and 4th quadrant,respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S.

Consider the circle x^2+y^2=9 and the parabola y^2=8x . They intersect at P and Q in the first and fourth quadrants, respectively. Tangents to the circle at P and Q intersect the X-axis at R and tangents to the parabola at P and Q intersect the X-axis at S. The ratio of the areas of trianglePQS" and "trianglePQR is

Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x . They intersect at P and Q in first and fourth quadrant respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S.

Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x . They intersect at P and Q in first and fourth quadrant respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangents at the parabola at P and Q intersect the x-axis at S. The radius of the circumcircle of the triangle PRS is-

Consider a parabola x^2-4xy+4y^2-32x+4y+16=0 . The focus of the parabola (P) is