Class 12

Math

Co-ordinate Geometry

Parabola

In which of the following cases, a unique parabola will be obtained ?

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Show that the curve whose parametric coordinates are $x=t_{2}+t+l,y=t_{2}−t+1$ represents a parabola.

Â·If the normals of the parabola $y_{2}=4x$ drawn at the end points of its latus rectum are tangents to the circle $(x−3)_{2}(y+2)_{2}=r_{2}$ , then the value of $r_{2}$ is

Consider the parabola `y^(2)=12x` and match the following lists :

Let (x,y) be any point on the parabola $y_{2}=4x$. 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 $y_{2}=8x$ is $y=x+2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

Length of the latus rectum of the parabola $x +y =a $ 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, $x_{2}+y_{2}=a$, (i), $my=m_{2}x+a$, (P), $(m_{2}a ,m2a )$II, $x_{2}+a_{2}y_{2}=a$, (ii), $y=mx+am_{2}+1 $, (Q), $(m_{2}+1 −ma ,m_{2}+1 a )$III, $y_{2}=4ax$, (iii), $y=mx+a_{2}m_{2}−1 $, (R), $(a_{2}m_{2}+1 −a_{2}m ,a_{2}m_{2}+1 1 )$IV, $x_{2}−a_{2}y_{2}=a_{2}$, (iv), $y=mx+a_{2}m_{2}+1 $, (S), $(a_{2}m_{2}+1 −a_{2}m ,a_{2}m_{2}+1 −1 )$If a tangent to a suitable conic (Column 1) is found to be $y=x+8$and 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)