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Standard IX

Mathematics

Equations Representing Parallel lines

——————- is th...

Question

------------------- is the equation of y-axis.

x = 0

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y = 1

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y = -1

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y = 0

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Solution

The correct option is A
x = 0

x = 0, is the equation of y axis.

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Similar questions

Q. The equation of line parallel to y-axis is:

(a) x = 1
(b) x + y = 0
(c) y = 0
(d) y = 1

S (x, y) = 0

represent a circle. The equation

S (x, 2) = 0

gives two identical solutions

x = 1

and the equation

S (1, y) = 0

gives two distinct solutions

y = 0, 2

. the equation of the circle is

Q. The equation to a coaxial system whose two members are

S_{1} = 0

and

S_{2} = 0

is given by

A system of circles is said to be coaxial when every pair of circles has the same radical axis. For coaxial circles, we note that

(1)The centers of all coaxial circles lie in a straight line, which is

⊥

to the common radical axis

(2)Circles passing through two fixed points form a coaxial system with a line joining the points as a common radical axis.

(3)The equation to a coaxial system whose two members are

S_{1} = 0

S_{2} = 0

is given by

S_{1} + λ S_{2} = 0, λ

is parameter.

If we take line of centres as x -axis & common radical axis as y-axis, then the simplest form of equation of coaxial circles is given by

x^{2} + y^{2} + 2 g x + c = 0

where

g

is variable &

c

is constant

g = \pm \sqrt{c}

then radious

g^{2} - c

vanishes & the circle become a point circle. The points

(\pm \sqrt{c}, 0)

are called the limiting points of the system of coaxial circle given by

x^{2} + y^{2} + 2 g x + c = 0

On the basis of above information answer the following question:

The equation of radical axis of the system of coaxial circles

x^{2} + y^{2} + 2 a x + 2 b y + c + 2 λ (a x - b y + 1) = 0

The equation representing the y - axis is

(a) x = 0

(b) y = 0

(d) y = a

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------------------- is the equation of y-axis.

The correct option is A x = 0 x = 0, is the equation of y axis.

The correct option is A
x = 0

x = 0, is the equation of y axis.