In which of the following cases, a unique parabola will be obtained ?
Â·If the normals of the parabola y2=4x drawn at the end points of its latus rectum are tangents to the circle (x−3)2(y+2)2=r2 , then the value of r2 is
Let (x,y) be any point on the parabola y2=4x. Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :
If the points (2,3) and (3,2) on a parabola are equidistant from the focus, then the slope of its tangent at vertex is
The equation of a tangent to the parabola y2=8x is y=x+2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is
Column 1,2 and 3 contains conics, equations of tangents to the conics and points of contact, respectively.Column I, Column 2, Column 3I, x2+y2=a, (i), my=m2x+a, (P), (m2a,m2a)II, x2+a2y2=a, (ii), y=mx+am2+1, (Q), (m2+1−ma,m2+1a)III, y2=4ax, (iii), y=mx+a2m2−1, (R), (a2m2+1−a2m,a2m2+11)IV, x2−a2y2=a2, (iv), y=mx+a2m2+1, (S), (a2m2+1−a2m,a2m2+1−1)If a tangent to a suitable conic (Column 1) is found to be y=x+8and its point of contact is (8,16), then which of the followingoptions is the only CORRECT combination?(III) (ii) (Q) (b) (II) (iv) (R)(I) (ii) (Q) (d) (III) (i) (P)