The distance between the points (a +b ,0) and (0,a -b ), is : - Vidyadip

MCQ

The distance between the points $(\text{a}\cos\theta+\text{b}\sin\theta,0)$ and $(0,\text{a}\sin\theta-\text{b}\cos\theta),$ is :

A
$\text{a}^2+\text{b}^2$
B
$\text{a}^2-\text{b}^2$
✓
$\sqrt{\text{a}^2+\text{b}^2}$
D
$\sqrt{\text{a}^2-\text{b}^2}$

✓

Answer

Correct option: C.

$\sqrt{\text{a}^2+\text{b}^2}$

Since by the distance formula,
The distance between the points $(\text{a}\cos\theta+\text{b}\sin\theta,0)$ and $(0,\text{a}\sin\theta-\text{b}\cos\theta)$ is,
$\text{D}=\sqrt{(0-\text{a}\cos\theta-\text{b}\sin\theta)^2+(\text{a}\sin\theta-\text{b}\cos\theta-0)}$
$=\sqrt{(-\text{a}\cos\theta-\text{b}\sin\theta)^2+(\text{a}\sin\theta-\text{b}\cos\theta)^2}$
$=((\text{x}\pm\text{y})^2=\text{x}^2+2\text{xy}+\text{y}^2)$
$=\sqrt{\text{a}^2\cos^2\theta+2\text{ab}\sin\theta\cos\theta+\text{b}^2\sin^2\theta+ \text{a}^2\sin^2\theta-2\text{ab}\sin\theta\cos\theta+\text{b}^2\cos^2\theta}$
$=\sqrt{(\text{a}^2+\text{b}^2)\sin^2\theta+(\text{a}^2+\text{b}^2)\cos^2\theta}$
$=\sqrt{\text{a}^2+\text{b}^2(\sin^2\theta+\cos^2\theta)}$
$=\sqrt{\text{a}^2+\text{b}^2}$

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 "M.C.Q (1 Marks)" from Coordinate Geometry→Coordinate Geometry — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

A tower subtends an angle of $30^{\circ}$ at a point on the same level as its foot. At a second point $h$ metres above the first, the depression of the foot of the tower is $60^{\circ}$. The height of the tower is

Two numbers whose sum is 12 and the absolute value of whose difference is 4 are the roots of the equation ________.

If the probability of winning a game $0.4$ then the probability of losing it, is :

If $\text{a}\cos\theta+\text{b}\sin\theta=\text{m}$ and $\text{a}\sin\theta-\text{b}\cos\theta=\text{n},$ then $a^2+ b^2=$

In the figure, if $TP$ and $TQ$ are tangents drawn from an external point $T$ to a circle with centre $O$ such that $\angle\text{TQP}=60^\circ,$ then :

If $x = 1$ is a common roots of the equations $a x^2+a x+3=0,$ and $x^2+x+b=0,$ then $ab =$

If $n$th term of an A.P. is $(2 n+1)$, then the sum of first $n$ terms of the A.P. is

For what value of $t, x=\frac{2}{3}$ is a root of $7 x^2+t x-3=0$ ?

The modal value is the value of the variate which divides the total frequency into two equal parts :

The distance between the points $(\text{a}\cos25^\circ,0)$ and $(0,\text{a}\cos65^\circ)$ is: