Given : A circle, 2x^2+""2y^2=""5and a parabola, y^2=""4sqrt(5)""x | Filo

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class 11 Math Co-ordinate Geometry Parabola

Given : A circle,

2 x^{2} + 2 y^{2} = 5

and a parabola,

y^{2} = 45 x

.Statement - I : An equation of a common tangent to these curves is

y = x+ 5

Statement - II : If the line,

y = m x + \frac{5}{m} (m \neq = 0)

is their common tangent, then m satisfies

m^{4} - 3 m^{2} + 2 = 0 .

(a)

Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

(b)

Statement -I is True; Statement -II is False.

(c)

Statement -I is False; Statement -II is True

(d)

Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Correct answer: (a)

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straight lines

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Related Questions

If two tangents drawn from a point P to the parabola

y^{2} = 4 x

are at right angles, then the locus of P is

(a)

(b)

(c)

(d)

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A parabola is drawn through two given points

A (1, 0)

B (- 1, 0)

such that its directrix always touches the circle

x^{2} + y^{2} = 4

. Then
The maximum possible length of semilatus rectum is

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Tangents are drawn from any point on the line

x + 4 a = 0

to the parabola

y^{2} = 4 a x ˙

Then find the angle subtended by the chord of contact at the vertex.

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If length of focal chord

P Q

l,

p

is the perpendicular distance of

P Q

from the vertex of the parabola, then prove that

l \propto \frac{1}{p ^{2}} ˙

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Find the locus of the point of intersection of the perpendicular tangents of the curve

y^{2} + 4 y - 6 x - 2 = 0

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If the normals from any point to the parabola

y^{2} = 4 x

x = 2

at points whose ordinates are in AP, then prove that the slopes of tangents at the co-normal points are in GP.

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The equation of aparabola is

y^{2} = 4 x \dot{P} (1, 3)

Q (1, 1)

are two points in the

x y - p l a n e ˙

Then, for the parabola. (a)

P

Q

are exterior points. (b)

P

is an interior point while

Q

is an exterior point (c)

P

Q

are interior points. (d)

P

is an exterior point while

Q

is an interior point

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y = 2 x + 3

is a tangent to the parabola

y^{2} = 24 x,

then find its distance from the parallel normal.

play button image

Related Questions

If two tangents drawn from a point P to the parabola

y^{2} = 4 x

are at right angles, then the locus of P is

(a)

(b)

(c)

(d)

play button image

A parabola is drawn through two given points

A (1, 0)

B (- 1, 0)

such that its directrix always touches the circle

x^{2} + y^{2} = 4

. Then
The maximum possible length of semilatus rectum is

play button image

Tangents are drawn from any point on the line

x + 4 a = 0

to the parabola

y^{2} = 4 a x ˙

Then find the angle subtended by the chord of contact at the vertex.

play button image

If length of focal chord

P Q

l,

p

is the perpendicular distance of

P Q

from the vertex of the parabola, then prove that

l \propto \frac{1}{p ^{2}} ˙

play button image

Find the locus of the point of intersection of the perpendicular tangents of the curve

y^{2} + 4 y - 6 x - 2 = 0

play button image

If the normals from any point to the parabola

y^{2} = 4 x

x = 2

at points whose ordinates are in AP, then prove that the slopes of tangents at the co-normal points are in GP.

play button image

The equation of aparabola is

y^{2} = 4 x \dot{P} (1, 3)

Q (1, 1)

are two points in the

x y - p l a n e ˙

Then, for the parabola. (a)

P

Q

are exterior points. (b)

P

is an interior point while

Q

is an exterior point (c)

P

Q

are interior points. (d)

P

is an exterior point while

Q

is an interior point

play button image

y = 2 x + 3

is a tangent to the parabola

y^{2} = 24 x,

then find its distance from the parallel normal.

play button image

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Blog
Micro Class
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About Us
Contact Us
Privacy Policy and Terms & Conditions

Copyright FILO EDTECH PVT. LTD. 2021