IPMAT Indore 2022 - QA (MCQ) Q34 Explanation

Explanation:

(c)

Equation of ellipse x^/a^2 +y^2/b^2 = 1

& Equation of hyperbola x^2/a^2 − y^2/b^2 = 1

The equation of the given curve is x^2/sin√2 − sin√3 + y^2/cos√2 − cos√3 = 1

We know, foci always lies on major axis.

Also,

If a > b ⇒ 𝑥−𝑎𝑥𝑖𝑠 will be the major axis &

If b > a ⇒ 𝑦−𝑎𝑥𝑖𝑠 will be the major axis in both ellipse & hyperbola.

Here, we need to figure out which expression is greater between sin√2 − sin√3 and cos√2 − cos√3.

Note: Here √2 And √3 are the angles in radian and not degree.

Also, we know

√2 = 1.414

π/2 = 3.14/2 = 1.57

√3 = 1.732

From the graph, it is visible that,

sin√2 > sin√3

∴ sin√2 − sin√3 is always positive, but it will have a very small value.

(Because, 1.732 is farther from 1.57 compared to 1.414, which makes sin1.732 lesser than sin 1.414.)

Also from the graph, we can see that cos√3 will be a negative value. It means, cos√2 − cos√3 will be always be a positive value & will have larger magnitude compared to sin√2 − sin√3.

Thus, we can say that major axis, of given curve is y – axis & foci will be on this only.