If x=a and y=b , then b^2x^2 - a^2y^2 = - Vidyadip

MCQ

If $\text{x}=\text{a}\sec\theta \text{ and y}=\text{b}\tan\theta,$ then $b^2x^2 - a^2y^2 $=

A
$ab$
B
$a^2 - b^2$
C
$a^2 + b^2$
✓
$a^2b^2$

✓

Answer

Correct option: D.

$a^2b^2$

Given, $\text{x}=\text{a}\sec\theta,\text{y}=\text{b}\tan\theta$
So, $\text{b}^2\text{y}^2-\text{a}^2\text{y}^2$
$=\text{b}^2(\text{a}\sec\theta)^2-\text{a}^2(\text{b}\tan\theta)^2$
$=\text{b}^2\text{a}^2\sec^2\theta-\text{a}^2\text{b}^2\tan^2\theta$
$=\text{b}^2\text{a}^2(\sec^2\theta-\tan^2\theta)$
We know that,
$\sec^2\theta-\tan^2\theta=1$
$\text{b}^2\text{x}^2-\text{a}^2\text{y}^2=\text{a}^2\text{b}^2$
Hence, the correct option is $(D).$

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 Trigonometric Identities→Trigonometric Identities — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of orginal cylinder is:

The area of $\triangle\text{ABC}$ with vertice $A(a, 0), O(0, 0)$ and $B(0, b)$ in square units is:

70 shares of FV 100 each are purchased for MV Rs.130 then the sum invested is..........

The lenght of the hypotenuse of an isosceles right triangle whose one side is $4\sqrt{2}\text{cm}$ is:

The decimal expansion of the rational number $\frac{33}{2^2\times5}$ will terminate after:

If the mean of the following distribution is $2.6,$ then the value of $y$ is:

Varible $(x)$	$1$	$2$	$3$	$4$	$5$
Fraquency	$4$	$5$	$y$	$1$	$2$

The roots of x² + kx + k = 0 are real and equal, find k.

The areas of two similar triangles $\triangle\text{ABC}$ and $\triangle\text{DEF}$ are $144cm^2$ and $81cm^2$ respectively. If the longest side of larger $\triangle\text{ABC}$ be $36\ cm$, then the longest side of the smaller triangle $\triangle\text{DEF}$ is:

A bag contains cards numbered from $1$ to $25$. A card is drawn at random from the bag. The probability that the number on this card is divisible by both $2$ and $3$ is:

The area of the sector of angle $\theta^\circ$ of a circle with radius $R$ is: