CUET PG 2026 — Mathematics PYQ

Solution

The length of the latus rectum for a parabola in the standard form $(y-k{)}^2=4a(x-h)$ or $(x-h{)}^2=4a(y-k)$ is equal to the absolute value of the coefficient of the linear term, which is $|4a|$.

1. Length for (A):

Equation: $y^2=8x$

This is in the form $y^2=4ax$.

$4a=8$

Length of Latus Rectum (A) = 8

2. Length for (B):

Equation: $4x^2+y=0⟹4x^2=-y⟹x^2=-\frac{1}{4}y$

This is in the form $x^2=-4ay$.

$4a=\frac{1}{4}$

Length of Latus Rectum (B) = 0.25

3. Length for (C):

Equation: $y^2-4y-3x+1=0$

Complete the square for $y$:

$(y^2-4y+4)-4-3x+1=0$

$(y-2{)}^2=3x+3⟹(y-2{)}^2=3(x+1)$

The coefficient of the linear term $(x+1)$ is 3.

Length of Latus Rectum (C) = 3

4. Length for (D):

Equation: $y^2-4y+4x=0$

Complete the square for $y$:

$(y^2-4y+4)-4+4x=0$

$(y-2{)}^2=-4x+4⟹(y-2{)}^2=-4(x-1)$

The absolute value of the coefficient of the linear term $(x-1)$ is 4.

Length of Latus Rectum (D) = 4

Comparison of Lengths:

• (B) = 0.25

• (C) = 3

• (D) = 4

• (A) = 8

Increasing Order: B < C < D < A

Correct Option: (d)