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Standard VI

Mathematics

Circle

The point whi...

Question

The point which bisects every chord of the conic passing through it, is called the centre of the conic.

True

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False

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True only for circles

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True only for parabola, ellipse, hyperbola

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Solution

The correct option is A True
Definition of center of conics states that, The point which bisects every chord of the conic passing through it is called center of the conic, hence the given statement is true for easy understanding consider the above image too which shows the point which bisects every chord of the conic passing through it is called center of the conic.

Suggest Corrections

Similar questions

Q. Assertion :Any chord of ellipse

x^{2} + y^{2} + x y = 1

through origin is bisected at origin. Reason: The centre of the ellipse is a point through which every chord is bisected.

Q. Assertion :Any chord of the ellipse

x^{2} + y^{2} + x y = 1

through

(0, 0)

is bisected at

(0, 0)

Reason: The centre of an ellipse is a point through which every chord is bisected.

Q. If the focus is

(α, β)

& the directrix is

a x + b y + c = 0

then the equation of conic whose eccentricity

= e

is given by

{(x - α)}^{2} + {(y - β)}^{2} = e^{2} \frac{{(a x + b y + c)}^{2}}{a^{2} + b^{2}}

. If

e = 1

then conic is called parabola, for

e < 1

(conic is an ellipse) and for

e > 1,

conic is a hyperbola.

Now consider the conic

169 {{(x - 1)}^{2} + {(y - 3)}^{2}} = {(5 x - 12 y + 17)}^{2}

......

(*)

On the basis of above information answer the following question:

The equation of axis of the conic

(*)

If the focus is

(α, β)

& the directrix is

a x + b y + c = 0

then the equation of conic whose eccentricity

= e

is given by

{(x - α)}^{2} + {(y - β)}^{2} = e^{2} \frac{{(a x + b y + c)}^{2}}{a^{2} + b^{2}}

. If

e = 1

then conic is called parabola, for

e < 1

(conic is an ellipse) and for

e > 1,

conic is a hyperbola.

Now consider the conic

169 {{(x - 1)}^{2} + {(y - 3)}^{2}} = {(5 x - 12 y + 17)}^{2}

......

(*)

On the basis of above information answer the following question:

The equation of directrix of the conic

(*)

A conic C passing through

P (1, 2)

is such that the slope of its tangent at any point on the conic is inversely proportional to the ordinate of that point and conic C passes through origin.

If a circle touches the conic C at the point

P (1, 2)

and passes through the focus of the conic then its radius is-

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