Download App

rectangular cartensian co-ordinates — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
Two points $A$ and $B$ have coordinates $(1, 0)$ and $(-1, 0)$ respectively and $Q$ is a point which satisfies the relation $AQ - BQ = $ $ \pm 1.$The locus of $Q$ is
  • A
    $12{x^2} + 4{y^2} = 3$
  • ✓
    $12{x^2} - 4{y^2} = 3$
  • C
    $12{x^2} - 4{y^2} + 3 = 0$
  • D
    $12{x^2} + 4{y^2} + 3 = 0$
✓

Answer

Correct option: B.
$12{x^2} - 4{y^2} = 3$
b
(b) According to the given condition

$\sqrt {{{(x - 1)}^2} + {y^2}} - \sqrt {{{(x + 1)}^2} + {y^2}} = \pm 1$

On squaring both sides, we get

$2{x^2} + 2{y^2} + 1 = 2\sqrt {{{(x - 1)}^2} + {y^2}} .\sqrt {{{(x + 1)}^2} + {y^2}} $

Again on squaring, we get $12{x^2} - 4{y^2} = 3$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from rectangular cartensian co-ordinates→rectangular cartensian co-ordinates — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $x$ is real and satisfies $x + 2 > \sqrt {x + 4} ,$ then
→
Three numbers are chosen from 1 to 20. The probability that they are not consecutive is:
→
A die is rolled, then the probability that an even number is obtained is:
→
If the $x-$ intercept of some line $L$ is double as that of the line, $3x + 4y = 12$ and the $y-$ intercept of $L$ is half as that of the same line, then the slope of $L$ is
→
The point on the axis of parabola $3y^2+4y-6x+8=0$ from which $3$ real normals can be drawn is given by:
→
Let $n \geq 4$ be a positive integer and let $l_1, l_2, \ldots, l_n$ be the lengths of the sides of arbitrary $n$ sided non-degenerate polygon $P$. Suppose $\frac{l_1}{l_2}+\frac{l_2}{l_3}+\ldots+\frac{l_{n-1}}{l_n}+\frac{l_n}{l_1}=n$ Consider the following statements:

$I$. The lengths of the sides of $P$ are equal.

$II$. The angles of $P$ are equal.

$III.$ $P$ is a regular polygon if it is cyclic.

→
Choose the correct answer: Which of the following is not a statement.
→
The diagonals of a parallelogram $PQRS$ are along the lines $x + 3y = 4$ and $6x - 2y = 7$. Then $PQRS$ must be a
→
A bag contains tickets numbered from $1$ to $20$. Two tickets are drawn. The probability that both the numbers are prime, is
→
There is a rectangular sheet of dimension $(2m - 1) × (2n - 1)$, (where $m > 0,n > 0)$. It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length
→