IGDTUW 2026 — Mathematics PYQ

Step 1: Understand the given relationship

Let the length of the major axis of the ellipse be $2a$ and the length of the minor axis be $2b$.

According to the problem, the major axis is three times the minor axis:

$$2a=3(2b)$$

Dividing both sides by 2, we get:

$$a=3b$$

Step 2: Use the eccentricity formula

The relationship between the semi-major axis $a$, semi-minor axis $b$, and eccentricity $e$ of an ellipse is given by the formula:

$$b^2=a^2(1-e^2)$$

Step 3: Substitute the value of $a$ into the formula

Substitute $a=3b$ into the eccentricity equation:

$$b^2=(3b{)}^2(1-e^2)$$

$$b^2=9b^2(1-e^2)$$

Step 4: Solve for eccentricity ($e$)

Divide both sides by $b^2$ (since $b\ne 0$):

$$1=9(1-e^2)$$

Now, open the bracket or divide by 9:

$$\frac{1}{9}=1-e^2$$

Rearrange the terms to solve for $e^2$:

$$e^2=1-\frac{1}{9}$$

$$e^2=\frac{9-1}{9}$$

$$e^2=\frac{8}{9}$$

Taking the square root on both sides:

$$e=\sqrt{\frac{8}{9}}$$

$$e=\frac{\sqrt{4\times 2}}{3}$$

$$e=\frac{2\sqrt{2}}{3}$$

Correct Answer

The correct option is (d).