If the segment intercepted by the parabo...

If the segment intercepted by the parabola `y=4a x` with the line `l x+m y+n=0` subtends a right angle at the vertex, then `4a l+n=0` (b) `4a l+4a m+n=0` `4a m+n=0` (d) `a l+n=0`

`4al+n=0`

`4al+4am+n=0`

`4am+n=0`

`al+n=0`

Text Solution

Verified by Experts

The correct Answer is:

Equation of pair of lines through origin
`y^(2)+4ax((lx+my)/(-n))" "` [Homogeneous equation of second degree]
`4alx^(2) +ny^(2) +4amxy=0`
These lines are perpendicular
`:.4al+n=0`

Similar Questions

Explore conceptually related problems

If the segment intercepted by the parabola y^2=4a x with the line l x+m y+n=0 subtends a right angle at the vertex, then 4a l+n=0 (b) 4a l+4a m+n=0 4a m+n=0 (d) a l+n=0

If the line l x+m y+n=0 touches the parabola y^2=4a x , prove that ln=a m^2

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.

The equation of the plane through the intersection of the plane a x+b y+c z+d=0\ a n d\ l x+m y+n+p=0 and parallel to the line y=0,\ z=0. (A) (b l-a m)y+(c l-a n)z+d l-a p=0 (B) (a m-b l)x+(m c-b n)z+m d-b p=0 (c) (n a-c l)d+(b n-c m)y+n d-c p=0 (D) None of these

If the line l x+m y+n=0 touches the circle x^2+y^2=a^2 , then prove that (l^2+m^2)a^2=n^2dot

Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at the vertex of the parabola. Then the tangents drawn to the parabola at A .and B will intersect at (a) (-4a ,0) (b) (-2a ,0) (-3a ,0) (d) none of these

The direction cosines l, m and n of two lines are connected by the relations l+m+n=0 and lm=0 , then the angle between the lines is

Show that the lines lx+my+n=0, mx+ny+l=0 and nx+ly+m=0 are concurrent if l+m+n=0

If the segment intercepted by the parabola `y=4a x` with the line `l x+m y+n=0` subtends a right angle at the vertex, then `4a l+n=0` (b) `4a l+4a m+n=0` `4a m+n=0` (d) `a l+n=0`

Text Solution

Similar Questions

Recommended Questions