A circle is drawn to pass through the extremities of the latus rectum of the parabola `y^2=8xdot` It is given that this circle also touches the direct

Question

A circle is drawn to pass through the extremities of the latus rectum of the parabola `y^2=8xdot` It is given that this circle also touches the direct

A circle is drawn to pass through the extremities of the latus rectum of the parabola `y^2=8xdot` It is given that this circle also touches the directrix of the parabola. Find the radius of this circle.

Monjur Alahi

6 views

2025-01-04 04:42

1 Answers

Related Questions

Normal is drawn at one of the extremities of the latus rectum of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` which meets the axes at points `Aa n dB` .

2 Answers 4 Views

Given the parabola `C : y = x^(2)`. If the circle at y axis with radius 1 touches parabola C at two distinct points, then find the coordinate of the c

2 Answers 5 Views

Find the equation of parabola (i) having focus at (0,-3) its directrix is y = 3. (ii) having end points of latus rectum (5,10) and (5,10) and which op

2 Answers 5 Views

The vertex of a parabola is (2, 2) and the coordinats of its two extremities of latus rectum are `(-2,0)` and (6, 0). Then find the equation of the pa

2 Answers 5 Views

The equation of the latus rectum of a parabola is `x+y=8` and the equation of the tangent at the vertex is `x+y=12.` Then find the length of the latus

2 Answers 5 Views

Find the length of the latus rectum of the parabola whose focus is at (2, 3) and directrix is the line `x-4y+3=0` .

2 Answers 4 Views

`y=x+2` is any tangent to the parabola `y^2=8xdot` The point `P` on this tangent is such that the other tangent from it which is perpendicular to it i

2 Answers 6 Views

The extremities of latus rectum of a parabola are (1, 1) and `(1,-1)` . Then the equation of the parabola can be `y^2=2x-1` (b) `y^2=1-2x` `y^2=2x-3`

2 Answers 6 Views

The locus of the midpoint of the focal distance of a variable point moving on theparabola `y^2=4a x` is a parabola whose latus rectum is half the latu

2 Answers 4 Views

Tangent to the parabola `y=x^(2)+ax+1` at the point of intersection of the y-axis also touches the circle `x^(2)+y^(2)=r^(2)`. Also, no point of the p

2 Answers 6 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 4
The extremities of the latus rectum are (2,4) and (2,-4).
Since any circle drawn with any focal chord as its diameter touches the directrix, the radius of the circle is 2a=4 (sincea=2).

6 views Answered 2023-02-05 15:29