A tangent to the parabola `y^2=8x` makes an angle of `45^0` with the straight line `y=3x+5.` Then find one of the points of contact.

Tangents are drawn to the hyperbola x^(2)/9 - y^(2)/4 parallel to the straight line 2x - y= 1 . One of the points of contact of tangents on the hyperbola is

If the normal chhord of the parabola y^(2)=4x makes an angle 45^(@) with the axis of the parabola, then its length, is

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.

Find the area bounded by the parabola y=x^2+1 and the straight line x+y=3.

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

Statement 1: The length of focal chord of a parabola y^2=8x making on an angle of 60^0 with the x-axis is 32. Statement 2: The length of focal chord of a parabola y^2=4a x making an angle with the x-axis is 4acos e c^2alpha

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. Tangents to the parabola y^(2)=4x at A and C intersect at point D and tangents to the parabola y^(2)=-8(x-a) intersect at point E. Then the area of quadrilateral DAEC is

From the point (4,6) , a pair of tangent lines is drawn to the parabola y^2=8 x . The area of the triangle formed by these pairs of tangent lines and the chord of contact of the point (4,6) is

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is