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

Question

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

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 rectum.

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Related Questions

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

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

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

2 Answers 6 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

If line `P Q` , where equation is `y=2x+k` , is a normal to the parabola whose vertex is `(-2,3)` and the axis parallel to the x-axis with latus rectu

2 Answers 7 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 is drawn at any point `(x_1, y_1)` other than the vertex on the parabola `y^2=4a x` . If tangents are drawn from any point on this tangent to

2 Answers 5 Views

The line `x+ y +2=0` is a tangent to a parabola at point A, intersect the directrix at B and tangent at vertex at C respectively. The focus of parabol

2 Answers 5 Views

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

Salim Ahmed Kawsar

Correct Answer - `8sqrt(2)`
Since the equation of latus rectum and the equation of tangent both are parallel, and the distance them is one - fourth of the latus rectum, the distance between them is
`a=|(-8+12)/(sqrt(1^(2)+1^(2)))|=(4)/(sqrt(2))=2sqrt(2)`
`:." Length of latus rectum"=4a=4(2sqrt(2))=8sqrt(2)`

5 views Answered 2023-02-05 15:29