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Byju's Answer

Standard XII

Mathematics

Distance between Two Parallel Planes

Let Sx, y, ...

Question

Let $S (x, y),$ such that $S$ is equidistant from points $O$ and $B$ with respect to new distance and if $x \geq 2$ and $0 \leq y < 3$ , then locus of $S$ is

a line segment

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a line

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a vertical ray

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a horizontal ray

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Solution

The correct option is C a horizontal ray
$d (O S) = d (B S)$
$| x - 0 | + | y - 0 | = | x - 2 | + | y - 3 |$
$x + y = x - 2 + 3 - y$
$(∵ x \geq 2$ & $0 \leq y < 3)$ .
$y = 1 / 2$ .
which is an infinite horizontal ray

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Similar questions

Q. For points

P \equiv (x_{1}, y_{1})

and

Q \equiv (x_{2}, y_{2})

of the coordinate plane, a new distance

d (P, Q) = | x_{1} - x_{2} | + | y_{1} - y_{2} |

Let

O \equiv (0, 0), A \equiv (2, 3)

and

C \equiv (4, 3)

are four fixed points on the

x - y

plane.
On the basis of the above information, answer the following questions:

Let

R (x, y)

such that

R

is equidistant from the points

O

and

A

with respect to new distance and if

0 \leq x < 1

and

0 \leq y < 2

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lie on a line segment whose equation is

Q. Locus of a point that is equidistant from the lines

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and

x + y - \sqrt{2} = 0

Q. For points

P = (x_{1}, y_{1}) and Q = (x_{2}, y_{2})

of the co-ordinate plane, a new distance

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d (P, Q) = | x_{1} - x_{2} | + | y_{1} - y_{2} |

. Let

O = (0, 0)

and

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The coordinates of the points O, A and B are (0, 0), (0, 4) and (6, 0) respectively. If a point P moves such that the

area of $△$ POA is always twice the area of $△$ POB, then the equation to the locus of P is

Q. A variable line

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L_{2} : x - y - 16 = 0

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Let S(x,y), such that S is equidistant from points O and B with respect to new distance and if x≥2 and 0≤y<3, then locus of S is

The correct option is C a horizontal rayd(OS)=d(BS)|x−0|+|y−0|=|x−2|+|y−3|x+y=x−2+3−y(∵x≥2 & 0≤y<3).y=1/2.which is an infinite horizontal ray

Let $S (x, y),$ such that $S$ is equidistant from points $O$ and $B$ with respect to new distance and if $x \geq 2$ and $0 \leq y < 3$ , then locus of $S$ is

The correct option is C a horizontal ray
$d (O S) = d (B S)$
$| x - 0 | + | y - 0 | = | x - 2 | + | y - 3 |$
$x + y = x - 2 + 3 - y$
$(∵ x \geq 2$ & $0 \leq y < 3)$ .
$y = 1 / 2$ .
which is an infinite horizontal ray