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Vertex

PQ is a doubl...

Question

PQ is a double ordinate of the parabola $y^{2} = 4 a x$ . If the normal at P intersect the line passing through Q and parallel to x-axis at G; then the locus of G is a parabola with

vertex at (4a, 0)

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focus at

(\sqrt{a}, 0)

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directrix as the line x - 3a = 0

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length of latus rectum equal to 4a.

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Solution

The correct options are
A vertex at (4a, 0)

C directrix as the line x - 3a = 0

D length of latus rectum equal to 4a.
Equation of normal at $P (a t^{2}, 2 a t)$ is

$y = - t x + 2 a t + a t^{3}$

$G (4 a + a t^{2}, - 2 a t)$
Locus of G(h, k) is

$y^{2} = 4 a (x - 4 a)$

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Similar questions

PQ is a double ordinate of the parabola $y^{2}$ = 4ax. If the normal at a point P intersects the line passing through Q and parallel to axis of the parabola at G. Then locus of G is a parabola with

P Q

is a double ordinate of the parabola

y^{2} = 4 a x

. If the normal at

P

intersect the line passing through

Q

and parallel to axis of

x

G

, then locus of

G

is a parabola with

Q. A variable chord

P Q

of the parabola

y^{2} = 4 a x

is drawn parallel to line

y = x

. Then the locus of point of intersection of normals at

P

and

Q

is:

P N P^{'}

is a double ordinate of the parabola ; prove that the locus of the point of intersection of the normal at

P

and the diameter through P' is the equal parabola

y^{2} = 4 a (x - 4 a) .

Q. The tangent PT and the normal PN to the parabola

y^{2} = 4 a x

at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola, whose

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PQ is a double ordinate of the parabola y2=4ax. If the normal at P intersect the line passing through Q and parallel to x-axis at G; then the locus of G is a parabola with

The correct options are A vertex at (4a, 0) C directrix as the line x - 3a = 0 D length of latus rectum equal to 4a. Equation of normal at P(at2,2at) is y=−tx+2at+at3 G(4a+at2,−2at) Locus of G(h, k) is y2=4a(x−4a)

PQ is a double ordinate of the parabola $y^{2} = 4 a x$ . If the normal at P intersect the line passing through Q and parallel to x-axis at G; then the locus of G is a parabola with

The correct options are
A vertex at (4a, 0)

C directrix as the line x - 3a = 0

D length of latus rectum equal to 4a.
Equation of normal at $P (a t^{2}, 2 a t)$ is

$y = - t x + 2 a t + a t^{3}$

$G (4 a + a t^{2}, - 2 a t)$
Locus of G(h, k) is

$y^{2} = 4 a (x - 4 a)$