Home
Class 12
MATHS
P is any point on the parabola, y^2=4ax ...

P is any point on the parabola, y^2=4ax whose vertex is A. PA is produced to meet the directrix in D & M is the foot of the perpendicular from P on the directrix. The angle subtended by MD at the focus is: (A) `pi/4` (B) `pi/3` (C) `(5pi)/12` (D) `pi/2`

Text Solution

Verified by Experts

`y-2at=(2at)/(at^2)(x-at^2)`
`y-2at=2/t(x-at^2)`
`y-2at=2/t(-a-at^2)`
`y=2at-(2a)/t-2at`
`y=-2a/t`
`y-2at=2x/t-2at`
`y=2x/t`
`y-2at=(-2at)/(2a)(x+a)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Pis a point on the parabola y^(2)=4ax(a<0) whose vertex is A.PA is produced to meet the directrix in M is the foot of the perpendicular from P on the directrix.If a circle is described on MD as a diameter then it intersects the X- axis at a point whose co-ordinates are:

P is the point on the parabola y^(2)=4ax(a>0) whose vertex is A .PA produced to meet the directrix in D and M is the foot of perpendicular from P on the directrix. If a circle is described on MD as a diameter, then its intersect x -axis at a point whose coordinates are

Let P be a point on the parabola y^(2) = 4ax with focus F . Let Q denote the foot of the perpendicular from P onto the directrix . Then (tan anglePQF)/(tananglePFQ) is_

If P be a point on the parabola y^(2)=4ax with focus F. Let Q denote the foot of the perpendicular from P onto the directrix.Then,(tan/_PQF)/(tan/_PFQ) is

The focus of a parabola is (2,3) and the foot of the perpendicular from the focus to the directrix is (4,5) . The equation to the parabola is .

y= -2x+12a is a normal to the parabola y^(2)=4ax at the point whose distance from the directrix of the parabola is

If a point P on y^2=4x , the foot of the perpendicular from P on the directrix and the focus form an equilateral traingle , then the coordinates of P may be

If a point P on y^2=4x , the foot of the perpendicular from P on the directrix and the focus form an equilateral traingle , then the coordinates of P may be

T is a point on the tangent to a parabola y^(2) = 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then

A line of slope lambda(0 lt lambda lt 1) touches the parabola y+3x^2=0 at P . If S is the focus and M is the foot of the perpendicular of directrix from P , then tan/_M P S